The document defines key statistical terms and concepts including:
- Sampling mean is an estimate of the population mean based on a sample. It is calculated by adding all values and dividing by the sample size.
- Sample variance measures the variation or spread of values in a sample. It is calculated by finding the mean of squared differences from the sample mean.
- Standard deviation is the square root of the variance, providing a measure of dispersion from the mean.
- Hypothesis testing uses sample data to determine the validity of claims about a population. The null hypothesis is tested against an alternative using statistical significance.
- Decision trees visually represent decision problems by showing possible choices, outcomes, and probabilities to
SAMPLING MEAN DEFINITION The term sampling mean is.docxagnesdcarey33086
The document provides definitions and explanations of statistical concepts including:
- Sampling mean, which is an estimate of the population mean based on a sample.
- Sample variance, which measures the spread or variation of values in a sample from the sample mean.
- Standard deviation, which is the square root of the sample variance and measures how dispersed the values are from the mean.
- Hypothesis testing, which determines the validity of claims about a population by distinguishing rare events that occur by chance from those unlikely to occur by chance.
- Decision trees, which use a tree structure to systematically layout and analyze decisions and their potential consequences.
SAMPLING MEAN DEFINITION The term sampling mean .docxanhlodge
SAMPLING MEAN:
DEFINITION:
The term sampling mean is a statistical term used to describe the properties of statistical
distributions. In statistical terms, the sample mean from a group of observations is an
estimate of the population mean . Given a sample of size n, consider n independent random
variables X1, X2... Xn, each corresponding to one randomly selected observation. Each of these
variables has the distribution of the population, with mean and standard deviation . The
sample mean is defined to be
WHAT IT IS USED FOR:
It is also used to measure central tendency of the numbers in a database. It can also be said that
it is nothing more than a balance point between the number and the low numbers.
HOW TO CALCULATE IT:
To calculate this, just add up all the numbers, then divide by how many numbers there are.
Example: what is the mean of 2, 7, and 9?
Add the numbers: 2 + 7 + 9 = 18
Divide by how many numbers (i.e., we added 3 numbers): 18 ÷ 3 = 6
So the Mean is 6
SAMPLE VARIANCE:
DEFINITION:
The sample variance, s2, is used to calculate how varied a sample is. A sample is a select number
of items taken from a population. For example, if you are measuring American people’s weights,
it wouldn’t be feasible (from either a time or a monetary standpoint) for you to measure the
weights of every person in the population. The solution is to take a sample of the population, say
1000 people, and use that sample size to estimate the actual weights of the whole population.
WHAT IT IS USED FOR:
The sample variance helps you to figure out the spread out in the data you have collected or are
going to analyze. In statistical terminology, it can be defined as the average of the squared
differences from the mean.
HOW TO CALCULATE IT:
Given below are steps of how a sample variance is calculated:
• Determine the mean
• Then for each number: subtract the Mean and square the result
• Then work out the mean of those squared differences.
To work out the mean, add up all the values then divide by the number of data points.
First add up all the values from the previous step.
But how do we say "add them all up" in mathematics? We use the Roman letter Sigma: Σ
The handy Sigma Notation says to sum up as many terms as we want.
• Next we need to divide by the number of data points, which is simply done by
multiplying by "1/N":
Statistically it can be stated by the following:
•
http://www.statisticshowto.com/find-sample-size-statistics/
http://www.mathsisfun.com/algebra/sigma-notation.html
• This value is the variance
EXAMPLE:
Sam has 20 Rose Bushes.
The number of flowers on each bush is
9, 2, 5, 4, 12, 7, 8, 11, 9, 3, 7, 4, 12, 5, 4, 10, 9, 6, 9, 4
Work out the sample variance
Step 1. Work out the mean
In the formula above, μ (the Greek letter "mu") is the mean of all our values.
For this example, the data points are: 9, 2, 5, 4, 12, 7, 8,.
Answer the questions in one paragraph 4-5 sentences. · Why did t.docxboyfieldhouse
Answer the questions in one paragraph 4-5 sentences.
· Why did the class collectively sign a blank check? Was this a wise decision; why or why not? we took a decision all the class without hesitation
· What is something that I said individuals should always do; what is it; why wasn't it done this time? Which mitigation strategies were used; what other strategies could have been used/considered? individuals should always participate in one group and take one decision
SAMPLING MEAN:
DEFINITION:
The term sampling mean is a statistical term used to describe the properties of statistical distributions. In statistical terms, the sample meanfrom a group of observations is an estimate of the population mean. Given a sample of size n, consider n independent random variables X1, X2... Xn, each corresponding to one randomly selected observation. Each of these variables has the distribution of the population, with mean and standard deviation. The sample mean is defined to be
WHAT IT IS USED FOR:
It is also used to measure central tendency of the numbers in a database. It can also be said that it is nothing more than a balance point between the number and the low numbers.
HOW TO CALCULATE IT:
To calculate this, just add up all the numbers, then divide by how many numbers there are.
Example: what is the mean of 2, 7, and 9?
Add the numbers: 2 + 7 + 9 = 18
Divide by how many numbers (i.e., we added 3 numbers): 18 ÷ 3 = 6
So the Mean is 6
SAMPLE VARIANCE:
DEFINITION:
The sample variance, s2, is used to calculate how varied a sample is. A sample is a select number of items taken from a population. For example, if you are measuring American people’s weights, it wouldn’t be feasible (from either a time or a monetary standpoint) for you to measure the weights of every person in the population. The solution is to take a sample of the population, say 1000 people, and use that sample size to estimate the actual weights of the whole population.
WHAT IT IS USED FOR:
The sample variance helps you to figure out the spread out in the data you have collected or are going to analyze. In statistical terminology, it can be defined as the average of the squared differences from the mean.
HOW TO CALCULATE IT:
Given below are steps of how a sample variance is calculated:
· Determine the mean
· Then for each number: subtract the Mean and square the result
· Then work out the mean of those squared differences.
To work out the mean, add up all the values then divide by the number of data points.
First add up all the values from the previous step.
But how do we say "add them all up" in mathematics? We use the Roman letter Sigma: Σ
The handy Sigma Notation says to sum up as many terms as we want.
· Next we need to divide by the number of data points, which is simply done by multiplying by "1/N":
Statistically it can be stated by the following:
·
· This value is the variance
EXAMPLE:
Sam has 20 Rose Bushes.
The number of flowers on each b.
A General Manger of Harley-Davidson has to decide on the size of a.docxevonnehoggarth79783
A General Manger of Harley-Davidson has to decide on the size of a new facility. The GM has narrowed the choices to two: large facility or small facility. The company has collected information on the payoffs. It now has to decide which option is the best using probability analysis, the decision tree model, and expected monetary value.
Options:
Facility
Demand Options
Probability
Actions
Expected Payoffs
Large
Low Demand
0.4
Do Nothing
($10)
Low Demand
0.4
Reduce Prices
$50
High Demand
0.6
$70
Small
Low Demand
0.4
$40
High Demand
0.6
Do Nothing
$40
High Demand
0.6
Overtime
$50
High Demand
0.6
Expand
$55
Determination of chance probability and respective payoffs:
Build Small:
Low Demand
0.4($40)=$16
High Demand
0.6($55)=$33
Build Large:
Low Demand
0.4($50)=$20
High Demand
0.6($70)=$42
Determination of Expected Value of each alternative
Build Small: $16+$33=$49
Build Large: $20+$42=$62
Click here for the Statistical Terms review sheet.
Submit your conclusion in a Word document to the M4: Assignment 2 Dropbox byWednesday, November 18, 2015.
A General Manger of Harley
-
Davidson has to decide on the size of a new facility. The GM has narrowed
the choices to two: large facility or small facility. The company has collected information on the payoffs. It
now has to decide which option is the best u
sing probability analysis, the decision tree model, and
expected monetary value.
Options:
Facility
Demand
Options
Probability
Actions
Expected
Payoffs
Large
Low Demand
0.4
Do Nothing
($10)
Low Demand
0.4
Reduce Prices
$50
High Demand
0.6
$70
Small
Low Demand
0.4
$40
High Demand
0.6
Do Nothing
$40
High Demand
0.6
Overtime
$50
High Demand
0.6
Expand
$55
A General Manger of Harley-Davidson has to decide on the size of a new facility. The GM has narrowed
the choices to two: large facility or small facility. The company has collected information on the payoffs. It
now has to decide which option is the best using probability analysis, the decision tree model, and
expected monetary value.
Options:
Facility
Demand
Options
Probability Actions
Expected
Payoffs
Large Low Demand 0.4 Do Nothing ($10)
Low Demand 0.4 Reduce Prices $50
High Demand 0.6
$70
Small Low Demand 0.4
$40
High Demand 0.6 Do Nothing $40
High Demand 0.6 Overtime $50
High Demand 0.6 Expand $55
SAMPLING MEAN:
DEFINITION:
The term sampling mean is a statistical term used to describe the properties of statistical distributions. In statistical terms, the sample meanfrom a group of observations is an estimate of the population mean. Given a sample of size n, consider n independent random variables X1, X2... Xn, each corresponding to one randomly selected observation. Each of these variables has the distribution of the population, with mean and standard deviation. The sample mean is defined to be
WHAT IT IS USED FOR:
It is also used to measure central tendency of the numbers in a .
The document discusses different types of data distributions including normal, binomial, Poisson, exponential, and Bernoulli distributions. It provides the formulas and properties of each distribution. For example, it states that the normal distribution is the most commonly used in data science and has a bell-shaped, symmetric curve. The Poisson distribution outlines the probability of events in fixed time periods and has a rate parameter λ. The exponential distribution gives the probability of time before an event and uses the rate parameter in its formula.
Descriptive statistics are used to summarize and describe characteristics of a data set. It includes measures of central tendency like mean, median, and mode, measures of variability like range and standard deviation, and the distribution of data through histograms. Inferential statistics are used to generalize results from a sample to the population it represents through estimation of population parameters and hypothesis testing. Correlation and regression analysis are used to study relationships between two or more variables.
This document discusses descriptive statistics and summarizing distributions. It covers measures of central tendency including the mean, median, and mode. It also discusses measures of dispersion such as variance and standard deviation. These measures are used to describe the characteristics of frequency distributions and determine where the center is located and how spread out the data is. The choice between measures depends on whether the distribution is normal or skewed.
SAMPLING MEAN DEFINITION The term sampling mean is.docxagnesdcarey33086
The document provides definitions and explanations of statistical concepts including:
- Sampling mean, which is an estimate of the population mean based on a sample.
- Sample variance, which measures the spread or variation of values in a sample from the sample mean.
- Standard deviation, which is the square root of the sample variance and measures how dispersed the values are from the mean.
- Hypothesis testing, which determines the validity of claims about a population by distinguishing rare events that occur by chance from those unlikely to occur by chance.
- Decision trees, which use a tree structure to systematically layout and analyze decisions and their potential consequences.
SAMPLING MEAN DEFINITION The term sampling mean .docxanhlodge
SAMPLING MEAN:
DEFINITION:
The term sampling mean is a statistical term used to describe the properties of statistical
distributions. In statistical terms, the sample mean from a group of observations is an
estimate of the population mean . Given a sample of size n, consider n independent random
variables X1, X2... Xn, each corresponding to one randomly selected observation. Each of these
variables has the distribution of the population, with mean and standard deviation . The
sample mean is defined to be
WHAT IT IS USED FOR:
It is also used to measure central tendency of the numbers in a database. It can also be said that
it is nothing more than a balance point between the number and the low numbers.
HOW TO CALCULATE IT:
To calculate this, just add up all the numbers, then divide by how many numbers there are.
Example: what is the mean of 2, 7, and 9?
Add the numbers: 2 + 7 + 9 = 18
Divide by how many numbers (i.e., we added 3 numbers): 18 ÷ 3 = 6
So the Mean is 6
SAMPLE VARIANCE:
DEFINITION:
The sample variance, s2, is used to calculate how varied a sample is. A sample is a select number
of items taken from a population. For example, if you are measuring American people’s weights,
it wouldn’t be feasible (from either a time or a monetary standpoint) for you to measure the
weights of every person in the population. The solution is to take a sample of the population, say
1000 people, and use that sample size to estimate the actual weights of the whole population.
WHAT IT IS USED FOR:
The sample variance helps you to figure out the spread out in the data you have collected or are
going to analyze. In statistical terminology, it can be defined as the average of the squared
differences from the mean.
HOW TO CALCULATE IT:
Given below are steps of how a sample variance is calculated:
• Determine the mean
• Then for each number: subtract the Mean and square the result
• Then work out the mean of those squared differences.
To work out the mean, add up all the values then divide by the number of data points.
First add up all the values from the previous step.
But how do we say "add them all up" in mathematics? We use the Roman letter Sigma: Σ
The handy Sigma Notation says to sum up as many terms as we want.
• Next we need to divide by the number of data points, which is simply done by
multiplying by "1/N":
Statistically it can be stated by the following:
•
http://www.statisticshowto.com/find-sample-size-statistics/
http://www.mathsisfun.com/algebra/sigma-notation.html
• This value is the variance
EXAMPLE:
Sam has 20 Rose Bushes.
The number of flowers on each bush is
9, 2, 5, 4, 12, 7, 8, 11, 9, 3, 7, 4, 12, 5, 4, 10, 9, 6, 9, 4
Work out the sample variance
Step 1. Work out the mean
In the formula above, μ (the Greek letter "mu") is the mean of all our values.
For this example, the data points are: 9, 2, 5, 4, 12, 7, 8,.
Answer the questions in one paragraph 4-5 sentences. · Why did t.docxboyfieldhouse
Answer the questions in one paragraph 4-5 sentences.
· Why did the class collectively sign a blank check? Was this a wise decision; why or why not? we took a decision all the class without hesitation
· What is something that I said individuals should always do; what is it; why wasn't it done this time? Which mitigation strategies were used; what other strategies could have been used/considered? individuals should always participate in one group and take one decision
SAMPLING MEAN:
DEFINITION:
The term sampling mean is a statistical term used to describe the properties of statistical distributions. In statistical terms, the sample meanfrom a group of observations is an estimate of the population mean. Given a sample of size n, consider n independent random variables X1, X2... Xn, each corresponding to one randomly selected observation. Each of these variables has the distribution of the population, with mean and standard deviation. The sample mean is defined to be
WHAT IT IS USED FOR:
It is also used to measure central tendency of the numbers in a database. It can also be said that it is nothing more than a balance point between the number and the low numbers.
HOW TO CALCULATE IT:
To calculate this, just add up all the numbers, then divide by how many numbers there are.
Example: what is the mean of 2, 7, and 9?
Add the numbers: 2 + 7 + 9 = 18
Divide by how many numbers (i.e., we added 3 numbers): 18 ÷ 3 = 6
So the Mean is 6
SAMPLE VARIANCE:
DEFINITION:
The sample variance, s2, is used to calculate how varied a sample is. A sample is a select number of items taken from a population. For example, if you are measuring American people’s weights, it wouldn’t be feasible (from either a time or a monetary standpoint) for you to measure the weights of every person in the population. The solution is to take a sample of the population, say 1000 people, and use that sample size to estimate the actual weights of the whole population.
WHAT IT IS USED FOR:
The sample variance helps you to figure out the spread out in the data you have collected or are going to analyze. In statistical terminology, it can be defined as the average of the squared differences from the mean.
HOW TO CALCULATE IT:
Given below are steps of how a sample variance is calculated:
· Determine the mean
· Then for each number: subtract the Mean and square the result
· Then work out the mean of those squared differences.
To work out the mean, add up all the values then divide by the number of data points.
First add up all the values from the previous step.
But how do we say "add them all up" in mathematics? We use the Roman letter Sigma: Σ
The handy Sigma Notation says to sum up as many terms as we want.
· Next we need to divide by the number of data points, which is simply done by multiplying by "1/N":
Statistically it can be stated by the following:
·
· This value is the variance
EXAMPLE:
Sam has 20 Rose Bushes.
The number of flowers on each b.
A General Manger of Harley-Davidson has to decide on the size of a.docxevonnehoggarth79783
A General Manger of Harley-Davidson has to decide on the size of a new facility. The GM has narrowed the choices to two: large facility or small facility. The company has collected information on the payoffs. It now has to decide which option is the best using probability analysis, the decision tree model, and expected monetary value.
Options:
Facility
Demand Options
Probability
Actions
Expected Payoffs
Large
Low Demand
0.4
Do Nothing
($10)
Low Demand
0.4
Reduce Prices
$50
High Demand
0.6
$70
Small
Low Demand
0.4
$40
High Demand
0.6
Do Nothing
$40
High Demand
0.6
Overtime
$50
High Demand
0.6
Expand
$55
Determination of chance probability and respective payoffs:
Build Small:
Low Demand
0.4($40)=$16
High Demand
0.6($55)=$33
Build Large:
Low Demand
0.4($50)=$20
High Demand
0.6($70)=$42
Determination of Expected Value of each alternative
Build Small: $16+$33=$49
Build Large: $20+$42=$62
Click here for the Statistical Terms review sheet.
Submit your conclusion in a Word document to the M4: Assignment 2 Dropbox byWednesday, November 18, 2015.
A General Manger of Harley
-
Davidson has to decide on the size of a new facility. The GM has narrowed
the choices to two: large facility or small facility. The company has collected information on the payoffs. It
now has to decide which option is the best u
sing probability analysis, the decision tree model, and
expected monetary value.
Options:
Facility
Demand
Options
Probability
Actions
Expected
Payoffs
Large
Low Demand
0.4
Do Nothing
($10)
Low Demand
0.4
Reduce Prices
$50
High Demand
0.6
$70
Small
Low Demand
0.4
$40
High Demand
0.6
Do Nothing
$40
High Demand
0.6
Overtime
$50
High Demand
0.6
Expand
$55
A General Manger of Harley-Davidson has to decide on the size of a new facility. The GM has narrowed
the choices to two: large facility or small facility. The company has collected information on the payoffs. It
now has to decide which option is the best using probability analysis, the decision tree model, and
expected monetary value.
Options:
Facility
Demand
Options
Probability Actions
Expected
Payoffs
Large Low Demand 0.4 Do Nothing ($10)
Low Demand 0.4 Reduce Prices $50
High Demand 0.6
$70
Small Low Demand 0.4
$40
High Demand 0.6 Do Nothing $40
High Demand 0.6 Overtime $50
High Demand 0.6 Expand $55
SAMPLING MEAN:
DEFINITION:
The term sampling mean is a statistical term used to describe the properties of statistical distributions. In statistical terms, the sample meanfrom a group of observations is an estimate of the population mean. Given a sample of size n, consider n independent random variables X1, X2... Xn, each corresponding to one randomly selected observation. Each of these variables has the distribution of the population, with mean and standard deviation. The sample mean is defined to be
WHAT IT IS USED FOR:
It is also used to measure central tendency of the numbers in a .
The document discusses different types of data distributions including normal, binomial, Poisson, exponential, and Bernoulli distributions. It provides the formulas and properties of each distribution. For example, it states that the normal distribution is the most commonly used in data science and has a bell-shaped, symmetric curve. The Poisson distribution outlines the probability of events in fixed time periods and has a rate parameter λ. The exponential distribution gives the probability of time before an event and uses the rate parameter in its formula.
Descriptive statistics are used to summarize and describe characteristics of a data set. It includes measures of central tendency like mean, median, and mode, measures of variability like range and standard deviation, and the distribution of data through histograms. Inferential statistics are used to generalize results from a sample to the population it represents through estimation of population parameters and hypothesis testing. Correlation and regression analysis are used to study relationships between two or more variables.
This document discusses descriptive statistics and summarizing distributions. It covers measures of central tendency including the mean, median, and mode. It also discusses measures of dispersion such as variance and standard deviation. These measures are used to describe the characteristics of frequency distributions and determine where the center is located and how spread out the data is. The choice between measures depends on whether the distribution is normal or skewed.
The document discusses measures of dispersion, which describe how varied or spread out a data set is around the average value. It defines several measures of dispersion, including range, interquartile range, mean deviation, and standard deviation. The standard deviation is described as the most important measure, as it takes into account all values in the data set and is not overly influenced by outliers. The document provides a detailed example of calculating the standard deviation, which involves finding the differences from the mean, squaring those values, summing them, and taking the square root.
- The document discusses key concepts in descriptive statistics including types of distributions, measures of central tendency, and measures of dispersion.
- It covers normal, skewed, and other types of distributions. Measures of central tendency discussed are mean, median, and mode. Measures of dispersion covered are variance and standard deviation.
- The document uses examples and explanations to illustrate how to calculate and interpret these important statistical measures.
- The document discusses key concepts in descriptive statistics including types of distributions, measures of central tendency, and measures of dispersion.
- It covers normal, skewed, and other types of distributions. Measures of central tendency discussed are mean, median, and mode. Measures of dispersion covered are variance and standard deviation.
- The document uses examples and explanations to illustrate how to calculate and interpret these important statistical measures.
This document discusses six measures of variation used to determine how values are distributed in a data set: range, quartile deviation, mean deviation, variance, standard deviation, and coefficient of variation. It provides definitions and examples of calculating each measure. The range is defined as the difference between the highest and lowest values. Quartile deviation uses the interquartile range (Q3-Q1). Mean deviation is the average of the absolute deviations from the mean. Variance and standard deviation measure how spread out values are from the mean, with variance using sums of squares and standard deviation taking the square root of variance.
These is info only ill be attaching the questions work CJ 301 – .docxmeagantobias
This document discusses measures of variability and dispersion in descriptive statistics. It defines variability as how scores differ from each other or from the mean. Four measures of dispersion are discussed: range, mean deviation, variance, and standard deviation. Standard deviation is described as the average distance from the mean and the most commonly used measure. Examples are provided to demonstrate how to calculate standard deviation step-by-step. The standard deviation is then used to estimate what percentage of values fall within certain ranges from the mean based on the normal distribution curve.
Basic Statistical Descriptions of Data.pptxAnusuya123
This document provides an overview of 7 basic statistical concepts for data science: 1) descriptive statistics such as mean, mode, median, and standard deviation, 2) measures of variability like variance and range, 3) correlation, 4) probability distributions, 5) regression, 6) normal distribution, and 7) types of bias. Descriptive statistics are used to summarize data, variability measures dispersion, correlation measures relationships between variables, and probability distributions specify likelihoods of events. Regression models relationships, normal distribution is often assumed, and biases can influence analyses.
Module-2_Notes-with-Example for data sciencepujashri1975
The document discusses several key concepts in probability and statistics:
- Conditional probability is the probability of one event occurring given that another event has already occurred.
- The binomial distribution models the probability of success in a fixed number of binary experiments. It applies when there are a fixed number of trials, two possible outcomes, and the same probability of success on each trial.
- The normal distribution is a continuous probability distribution that is symmetric and bell-shaped. It is characterized by its mean and standard deviation. Many real-world variables approximate a normal distribution.
- Other concepts discussed include range, interquartile range, variance, and standard deviation. The interquartile range describes the spread of a dataset's middle 50%
CJ 301 – Measures of DispersionVariability Think back to the .docxmonicafrancis71118
CJ 301 – Measures of Dispersion/Variability
Think back to the description of measures of central tendency that describes these statistics as measures of how the data in a distribution are clustered, around what summary measure are most of the data points clustered.
But when comes to descriptive statistics and describing the characteristics of a distribution, averages are only half story. The other half is measures of variability.
In the most simple of terms, variability reflects how scores differ from one another. For example, the following set of scores shows some variability:
7, 6, 3, 3, 1
The following set of scores has the same mean (4) and has less variability than the previous set:
3, 4, 4, 5, 4
The next set has no variability at all – the scores do not differ from one another – but it also has the same mean as the other two sets we just showed you.
4, 4, 4, 4, 4
Variability (also called spread or dispersion) can be thought of as a measure of how different scores are from one another. It is even more accurate (and maybe even easier) to think of variability as how different scores are from one particular score. And what “score” do you think that might be? Well, instead of comparing each score to every other score in a distribution, the one score that could be used as a comparison is – that is right- the mean. So, variability becomes a measure of how much each score in a group of scores differs from the mean.
Remember what you already know about computing averages – that an average (whether it is the mean, the median or the mode) is a representative score in a set of scores. Now, add your new knowledge about variability- that it reflects how different scores are from one another. Each is important descriptive statistic. Together, these two (average and variability) can be used to describe the characteristics of a distribution and show how distribution differ from one another.
Measures of dispersion/variability describe how the data in a distribution are scattered or dispersed around, or from, the central point represented by the measure of central tendency.
We will discuss four different measures of dispersion, the range, the mean deviation, the variance, and the standard deviation.
RANGE
The range is a very simple measure of dispersion to calculate and interpret. The range is simply the difference between the highest score and the lowest score in a distribution.
Consider the following distribution that measures the “Age” of a random sample of eight police officers in a small rural jurisdiction.
Officer X = Age_
1 41
2 20
3 35
4 25
5 23
6 30
7 21
8 32
First, let’s calculate the mean as our measure of central tendency by adding the individual ages of each officer and dividing by the number of officers. The calculation is 227/8 = 28.375 years.
In general, the formula for the range is:
R=h-l
Where:
· r is the range
· h is the highest score in the .
The document discusses measurement uncertainties and how to report experimental results with associated uncertainties. It begins by explaining that any measurement without a statement of uncertainty is of limited usefulness. There are two main sources of uncertainties - systematic errors which produce consistently high or low results, and random uncertainties which produce about half high and half low results. Random uncertainties can be characterized statistically using concepts like the normal distribution and standard deviation. When reporting a measurement, both the best value (e.g. the mean) and its uncertainty (e.g. the standard deviation of multiple trials) should be provided. For derived quantities, the uncertainties in input measurements must be propagated to determine the overall uncertainty in the result.
The document discusses various measures used to describe the dispersion or variability in a data set. It defines dispersion as the extent to which values in a distribution differ from the average. Several measures of dispersion are described, including range, interquartile range, mean deviation, and standard deviation. The document also discusses measures of relative standing like percentiles and quartiles, and how they can locate the position of observations within a data set. The learning objectives are to understand how to describe variability, compare distributions, describe relative standing, and understand the shape of distributions using these measures.
1. Statistics is used to analyze data beyond what can be seen in maps and diagrams by using mathematical manipulation, which can reveal patterns that may otherwise go unnoticed.
2. It is important to justify any statistical techniques used and to only use techniques that are appropriate for the type of data.
3. Common methods for summarizing large data sets include calculating the mean, mode, and median. The mean is the average, the mode is the most frequent value, and the median is the middle value when the data is arranged from lowest to highest.
1. Statistics is used to analyze data beyond what can be seen in maps and diagrams by using mathematical manipulation, which can reveal patterns that may otherwise go unnoticed.
2. It is important to justify any statistical techniques used and to ensure the data is appropriate for the technique. Students should ask what the technique can prove and if the data is in the right format before performing calculations.
3. Common methods for summarizing a large data set are the mean, median, and mode. The mean is the average, the median is the middle value, and the mode is the most frequent value. These give a single value for the data but do not show the variation around that value.
This document provides an overview of descriptive statistics concepts and methods. It discusses numerical summaries of data like measures of central tendency (mean, median, mode) and variability (standard deviation, variance, range). It explains how to calculate and interpret these measures. Examples are provided to demonstrate calculating measures for sample data and interpreting what they say about the data distribution. Frequency distributions and histograms are also introduced as ways to visually summarize and understand the characteristics of data.
This document provides an introduction to statistics. It discusses what statistics is, the two main branches of statistics (descriptive and inferential), and the different types of data. It then describes several key measures used in statistics, including measures of central tendency (mean, median, mode) and measures of dispersion (range, mean deviation, standard deviation). The mean is the average value, the median is the middle value, and the mode is the most frequent value. The range is the difference between highest and lowest values, the mean deviation is the average distance from the mean, and the standard deviation measures how spread out values are from the mean. Examples are provided to demonstrate how to calculate each measure.
Lecture. Introduction to Statistics (Measures of Dispersion).pptxNabeelAli89
1) The document discusses various measures of dispersion used to quantify how spread out or varied a set of data values are from the average.
2) There are two types of dispersion - absolute dispersion measures how varied data values are in the original units, while relative dispersion compares variability between datasets with different units.
3) Common measures of absolute dispersion include range, variance, and standard deviation. Range is the difference between highest and lowest values, while variance and standard deviation take into account how far all values are from the mean.
This document provides an outline and summaries of topics related to error analysis:
- It outlines topics including binomial distribution, Poisson distribution, normal distribution, confidence interval, and least squares analysis.
- The binomial distribution section provides an example of calculating the probability of getting 2 and 3 heads out of 6 coin tosses.
- The normal distribution section explains how to calculate the probability of scoring between 90-110 on an IQ test with a mean of 100 and standard deviation of 10.
- The confidence interval section provides an example of calculating the 95% confidence interval for the population mean boiling temperature based on 6 sample measurements.
Detailed discussion about the types of statistics form Measures of Central Tendency, Measures of Dispersion, Skewness, Kurtosis, Probability Distributions and much more with their uses cases
This document discusses measures of central tendency and different methods for calculating averages. It begins by defining central tendency as a single value that represents the characteristics of an entire data set. Three common measures of central tendency are introduced: the mean, median, and mode. The document then focuses on explaining how to calculate the arithmetic mean, or average, including the direct method, shortcut method, and how it applies to discrete and continuous data series. Weighted averages are also covered. In summary, the document provides an overview of key concepts in measures of central tendency and how to calculate various types of averages.
This document provides an introduction to key concepts in statistics including mean, mode, median, range, variance, standard deviation, standard error, t-tests, and confidence intervals. It defines these terms and explains how to calculate them. For example, it explains that standard deviation measures how spread out values are from the mean and it is calculated by taking the square root of the variance. It also describes how confidence intervals and t-tests can be used to determine if two data sets are statistically different from one another.
This document discusses various statistical concepts and their applications in clinical laboratories. It defines descriptive statistics, statistical analysis, measures of central tendency (mean, median, mode), measures of variation (variance, standard deviation), probability distributions (binomial, Gaussian, Poisson), and statistical tests (t-test, chi-square, F-test). It provides examples of how these statistical methods are used to monitor laboratory test performance, interpret results, and compare different laboratory instruments and methods.
…if one of the primary purposes of education is to teach young .docxanhlodge
“…if one of the primary purposes of education is to teach young people the skills, knowledge, and critical awareness to become productive members of a diverse and democratic society, a broadly conceptualize multicultural education can have a decisive influence.” Textbook page 338.
What steps do you think schools can or should take to promote our democracy in today’s very diverse country?
Food festivals and celebrating a cultural holiday will not be accepted as an answer. Those are examples of tokenism to make the dominant culture feel like they are doing something. These two activities are fun and interesting, but not how we will strengthen our democracy.
.
✍Report OverviewIn this assignment, you will Document an.docxanhlodge
✍
Report Overview
In this assignment, you will
Document and reflect on your university education and on learning experiences outside of the university;
Articulate how your upper-level coursework is an integrated and individualized curriculum built around your interests; and
Highlight the experiences, skills, and projects that show what you can do.
A successful report submission will be the product of many hours of work over several weeks.
A report earning maximum available points will be a carefully curated and edited explanation of your work that provides tangible evidence of—and insights into—your competencies and capabilities over time. In each section of this report, you are (1) telling a story about your own abilities, and (2) providing specific examples and evidence that illustrate and support your claims.
✍
Required Report Sections
Here the sections are listed as they must appear in your final graded submission. You’ll arrange the sections in this order when
submitting
the final report BUT you won’t follow this order when
writing
drafts of each section.
Note that each section description contains a Pro Tip that tells you how to proceed with the work – what to attempt first, second, and third, etc.
❖ I. Statement of Purpose ❖
Step 1.
Read these four very different
examples of successful Statement of Purpose sections
.
Step 2.
Consider the differences in tone, style, level of detail etc. Your own statement of purpose may resemble one of these. Indeed, writing a first draft based on an example or combination of examples is a good idea. BUT don’t let these examples limit your thinking or personal expression. You may want to begin with a quote from a famous person, use a quote from your mom, or skip the quote. You may want to discuss your personal motivations or get right down to the facts. You may want to list your classes or discuss how your work-life led you to this path.
Step 3.
Write a rough draft – let’s call that Statement of Purpose 1.0. Write Statement of Purpose 1.0 as quickly as you can and then put it away until after you have completed most of the report. Forget about Statement of Purpose 1.0 until most of your report is at least in draft form.
Step 4.
Once you have a draft of all sections of your report, you are in a good position to revise Statement of Purpose 1. You are ready for Step 4. Take Statement of Purpose 1.0 out its dusty vault and hold it up to the sun. Ah. Now read your report draft and compare it to the claims you made in Statement of Purpose 1.0. Ask yourself these questions:
Does Statement of Purpose 1.0. accurately introduce my report?
Are there important ideas or representative experiences in the report that should be highlighted in the Statement of Purpose but aren’t? Remember this isn’t a treasure hunt where its your reader’s job to figure out what matters. It’s your job to show the reader what matters.
If Statement of Purpose 1.0. isn’t the best map it can be for th.
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The document discusses measures of dispersion, which describe how varied or spread out a data set is around the average value. It defines several measures of dispersion, including range, interquartile range, mean deviation, and standard deviation. The standard deviation is described as the most important measure, as it takes into account all values in the data set and is not overly influenced by outliers. The document provides a detailed example of calculating the standard deviation, which involves finding the differences from the mean, squaring those values, summing them, and taking the square root.
- The document discusses key concepts in descriptive statistics including types of distributions, measures of central tendency, and measures of dispersion.
- It covers normal, skewed, and other types of distributions. Measures of central tendency discussed are mean, median, and mode. Measures of dispersion covered are variance and standard deviation.
- The document uses examples and explanations to illustrate how to calculate and interpret these important statistical measures.
- The document discusses key concepts in descriptive statistics including types of distributions, measures of central tendency, and measures of dispersion.
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- The document uses examples and explanations to illustrate how to calculate and interpret these important statistical measures.
This document discusses six measures of variation used to determine how values are distributed in a data set: range, quartile deviation, mean deviation, variance, standard deviation, and coefficient of variation. It provides definitions and examples of calculating each measure. The range is defined as the difference between the highest and lowest values. Quartile deviation uses the interquartile range (Q3-Q1). Mean deviation is the average of the absolute deviations from the mean. Variance and standard deviation measure how spread out values are from the mean, with variance using sums of squares and standard deviation taking the square root of variance.
These is info only ill be attaching the questions work CJ 301 – .docxmeagantobias
This document discusses measures of variability and dispersion in descriptive statistics. It defines variability as how scores differ from each other or from the mean. Four measures of dispersion are discussed: range, mean deviation, variance, and standard deviation. Standard deviation is described as the average distance from the mean and the most commonly used measure. Examples are provided to demonstrate how to calculate standard deviation step-by-step. The standard deviation is then used to estimate what percentage of values fall within certain ranges from the mean based on the normal distribution curve.
Basic Statistical Descriptions of Data.pptxAnusuya123
This document provides an overview of 7 basic statistical concepts for data science: 1) descriptive statistics such as mean, mode, median, and standard deviation, 2) measures of variability like variance and range, 3) correlation, 4) probability distributions, 5) regression, 6) normal distribution, and 7) types of bias. Descriptive statistics are used to summarize data, variability measures dispersion, correlation measures relationships between variables, and probability distributions specify likelihoods of events. Regression models relationships, normal distribution is often assumed, and biases can influence analyses.
Module-2_Notes-with-Example for data sciencepujashri1975
The document discusses several key concepts in probability and statistics:
- Conditional probability is the probability of one event occurring given that another event has already occurred.
- The binomial distribution models the probability of success in a fixed number of binary experiments. It applies when there are a fixed number of trials, two possible outcomes, and the same probability of success on each trial.
- The normal distribution is a continuous probability distribution that is symmetric and bell-shaped. It is characterized by its mean and standard deviation. Many real-world variables approximate a normal distribution.
- Other concepts discussed include range, interquartile range, variance, and standard deviation. The interquartile range describes the spread of a dataset's middle 50%
CJ 301 – Measures of DispersionVariability Think back to the .docxmonicafrancis71118
CJ 301 – Measures of Dispersion/Variability
Think back to the description of measures of central tendency that describes these statistics as measures of how the data in a distribution are clustered, around what summary measure are most of the data points clustered.
But when comes to descriptive statistics and describing the characteristics of a distribution, averages are only half story. The other half is measures of variability.
In the most simple of terms, variability reflects how scores differ from one another. For example, the following set of scores shows some variability:
7, 6, 3, 3, 1
The following set of scores has the same mean (4) and has less variability than the previous set:
3, 4, 4, 5, 4
The next set has no variability at all – the scores do not differ from one another – but it also has the same mean as the other two sets we just showed you.
4, 4, 4, 4, 4
Variability (also called spread or dispersion) can be thought of as a measure of how different scores are from one another. It is even more accurate (and maybe even easier) to think of variability as how different scores are from one particular score. And what “score” do you think that might be? Well, instead of comparing each score to every other score in a distribution, the one score that could be used as a comparison is – that is right- the mean. So, variability becomes a measure of how much each score in a group of scores differs from the mean.
Remember what you already know about computing averages – that an average (whether it is the mean, the median or the mode) is a representative score in a set of scores. Now, add your new knowledge about variability- that it reflects how different scores are from one another. Each is important descriptive statistic. Together, these two (average and variability) can be used to describe the characteristics of a distribution and show how distribution differ from one another.
Measures of dispersion/variability describe how the data in a distribution are scattered or dispersed around, or from, the central point represented by the measure of central tendency.
We will discuss four different measures of dispersion, the range, the mean deviation, the variance, and the standard deviation.
RANGE
The range is a very simple measure of dispersion to calculate and interpret. The range is simply the difference between the highest score and the lowest score in a distribution.
Consider the following distribution that measures the “Age” of a random sample of eight police officers in a small rural jurisdiction.
Officer X = Age_
1 41
2 20
3 35
4 25
5 23
6 30
7 21
8 32
First, let’s calculate the mean as our measure of central tendency by adding the individual ages of each officer and dividing by the number of officers. The calculation is 227/8 = 28.375 years.
In general, the formula for the range is:
R=h-l
Where:
· r is the range
· h is the highest score in the .
The document discusses measurement uncertainties and how to report experimental results with associated uncertainties. It begins by explaining that any measurement without a statement of uncertainty is of limited usefulness. There are two main sources of uncertainties - systematic errors which produce consistently high or low results, and random uncertainties which produce about half high and half low results. Random uncertainties can be characterized statistically using concepts like the normal distribution and standard deviation. When reporting a measurement, both the best value (e.g. the mean) and its uncertainty (e.g. the standard deviation of multiple trials) should be provided. For derived quantities, the uncertainties in input measurements must be propagated to determine the overall uncertainty in the result.
The document discusses various measures used to describe the dispersion or variability in a data set. It defines dispersion as the extent to which values in a distribution differ from the average. Several measures of dispersion are described, including range, interquartile range, mean deviation, and standard deviation. The document also discusses measures of relative standing like percentiles and quartiles, and how they can locate the position of observations within a data set. The learning objectives are to understand how to describe variability, compare distributions, describe relative standing, and understand the shape of distributions using these measures.
1. Statistics is used to analyze data beyond what can be seen in maps and diagrams by using mathematical manipulation, which can reveal patterns that may otherwise go unnoticed.
2. It is important to justify any statistical techniques used and to only use techniques that are appropriate for the type of data.
3. Common methods for summarizing large data sets include calculating the mean, mode, and median. The mean is the average, the mode is the most frequent value, and the median is the middle value when the data is arranged from lowest to highest.
1. Statistics is used to analyze data beyond what can be seen in maps and diagrams by using mathematical manipulation, which can reveal patterns that may otherwise go unnoticed.
2. It is important to justify any statistical techniques used and to ensure the data is appropriate for the technique. Students should ask what the technique can prove and if the data is in the right format before performing calculations.
3. Common methods for summarizing a large data set are the mean, median, and mode. The mean is the average, the median is the middle value, and the mode is the most frequent value. These give a single value for the data but do not show the variation around that value.
This document provides an overview of descriptive statistics concepts and methods. It discusses numerical summaries of data like measures of central tendency (mean, median, mode) and variability (standard deviation, variance, range). It explains how to calculate and interpret these measures. Examples are provided to demonstrate calculating measures for sample data and interpreting what they say about the data distribution. Frequency distributions and histograms are also introduced as ways to visually summarize and understand the characteristics of data.
This document provides an introduction to statistics. It discusses what statistics is, the two main branches of statistics (descriptive and inferential), and the different types of data. It then describes several key measures used in statistics, including measures of central tendency (mean, median, mode) and measures of dispersion (range, mean deviation, standard deviation). The mean is the average value, the median is the middle value, and the mode is the most frequent value. The range is the difference between highest and lowest values, the mean deviation is the average distance from the mean, and the standard deviation measures how spread out values are from the mean. Examples are provided to demonstrate how to calculate each measure.
Lecture. Introduction to Statistics (Measures of Dispersion).pptxNabeelAli89
1) The document discusses various measures of dispersion used to quantify how spread out or varied a set of data values are from the average.
2) There are two types of dispersion - absolute dispersion measures how varied data values are in the original units, while relative dispersion compares variability between datasets with different units.
3) Common measures of absolute dispersion include range, variance, and standard deviation. Range is the difference between highest and lowest values, while variance and standard deviation take into account how far all values are from the mean.
This document provides an outline and summaries of topics related to error analysis:
- It outlines topics including binomial distribution, Poisson distribution, normal distribution, confidence interval, and least squares analysis.
- The binomial distribution section provides an example of calculating the probability of getting 2 and 3 heads out of 6 coin tosses.
- The normal distribution section explains how to calculate the probability of scoring between 90-110 on an IQ test with a mean of 100 and standard deviation of 10.
- The confidence interval section provides an example of calculating the 95% confidence interval for the population mean boiling temperature based on 6 sample measurements.
Detailed discussion about the types of statistics form Measures of Central Tendency, Measures of Dispersion, Skewness, Kurtosis, Probability Distributions and much more with their uses cases
This document discusses measures of central tendency and different methods for calculating averages. It begins by defining central tendency as a single value that represents the characteristics of an entire data set. Three common measures of central tendency are introduced: the mean, median, and mode. The document then focuses on explaining how to calculate the arithmetic mean, or average, including the direct method, shortcut method, and how it applies to discrete and continuous data series. Weighted averages are also covered. In summary, the document provides an overview of key concepts in measures of central tendency and how to calculate various types of averages.
This document provides an introduction to key concepts in statistics including mean, mode, median, range, variance, standard deviation, standard error, t-tests, and confidence intervals. It defines these terms and explains how to calculate them. For example, it explains that standard deviation measures how spread out values are from the mean and it is calculated by taking the square root of the variance. It also describes how confidence intervals and t-tests can be used to determine if two data sets are statistically different from one another.
This document discusses various statistical concepts and their applications in clinical laboratories. It defines descriptive statistics, statistical analysis, measures of central tendency (mean, median, mode), measures of variation (variance, standard deviation), probability distributions (binomial, Gaussian, Poisson), and statistical tests (t-test, chi-square, F-test). It provides examples of how these statistical methods are used to monitor laboratory test performance, interpret results, and compare different laboratory instruments and methods.
Similar to SAMPLING MEANDEFINITIONThe term sampling mean is a stati.docx (20)
…if one of the primary purposes of education is to teach young .docxanhlodge
“…if one of the primary purposes of education is to teach young people the skills, knowledge, and critical awareness to become productive members of a diverse and democratic society, a broadly conceptualize multicultural education can have a decisive influence.” Textbook page 338.
What steps do you think schools can or should take to promote our democracy in today’s very diverse country?
Food festivals and celebrating a cultural holiday will not be accepted as an answer. Those are examples of tokenism to make the dominant culture feel like they are doing something. These two activities are fun and interesting, but not how we will strengthen our democracy.
.
✍Report OverviewIn this assignment, you will Document an.docxanhlodge
✍
Report Overview
In this assignment, you will
Document and reflect on your university education and on learning experiences outside of the university;
Articulate how your upper-level coursework is an integrated and individualized curriculum built around your interests; and
Highlight the experiences, skills, and projects that show what you can do.
A successful report submission will be the product of many hours of work over several weeks.
A report earning maximum available points will be a carefully curated and edited explanation of your work that provides tangible evidence of—and insights into—your competencies and capabilities over time. In each section of this report, you are (1) telling a story about your own abilities, and (2) providing specific examples and evidence that illustrate and support your claims.
✍
Required Report Sections
Here the sections are listed as they must appear in your final graded submission. You’ll arrange the sections in this order when
submitting
the final report BUT you won’t follow this order when
writing
drafts of each section.
Note that each section description contains a Pro Tip that tells you how to proceed with the work – what to attempt first, second, and third, etc.
❖ I. Statement of Purpose ❖
Step 1.
Read these four very different
examples of successful Statement of Purpose sections
.
Step 2.
Consider the differences in tone, style, level of detail etc. Your own statement of purpose may resemble one of these. Indeed, writing a first draft based on an example or combination of examples is a good idea. BUT don’t let these examples limit your thinking or personal expression. You may want to begin with a quote from a famous person, use a quote from your mom, or skip the quote. You may want to discuss your personal motivations or get right down to the facts. You may want to list your classes or discuss how your work-life led you to this path.
Step 3.
Write a rough draft – let’s call that Statement of Purpose 1.0. Write Statement of Purpose 1.0 as quickly as you can and then put it away until after you have completed most of the report. Forget about Statement of Purpose 1.0 until most of your report is at least in draft form.
Step 4.
Once you have a draft of all sections of your report, you are in a good position to revise Statement of Purpose 1. You are ready for Step 4. Take Statement of Purpose 1.0 out its dusty vault and hold it up to the sun. Ah. Now read your report draft and compare it to the claims you made in Statement of Purpose 1.0. Ask yourself these questions:
Does Statement of Purpose 1.0. accurately introduce my report?
Are there important ideas or representative experiences in the report that should be highlighted in the Statement of Purpose but aren’t? Remember this isn’t a treasure hunt where its your reader’s job to figure out what matters. It’s your job to show the reader what matters.
If Statement of Purpose 1.0. isn’t the best map it can be for th.
☰Menu×NURS 6050 Policy and Advocacy for Improving Population H.docxanhlodge
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NURS 6050 Policy and Advocacy for Improving Population Health
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Module 1
Module 2
Module 3
Module 4
Module 5
Module 6
.
▪ Learning Outcomes1.Understand the basic concepts and termin.docxanhlodge
▪
Learning Outcomes:1.
Understand the basic concepts and terminology used in Strategic Management. (Lo 1.2)2.
Understand the Corporation Social Responsibility
(Lo 1.4).3.
Explain how executive leadership is an important part of strategic management (Lo 3.4)
✓
Question 1
: How does strategic management typically evolve in a corporation? (
1Mark)
✓
Question 2
: Discuss the influence of globalization, social responsibility and environmental sustainability on strategic management of a corporation.(
2 Marks
)
✓
Question 3:
In what ways can a corporation’s structure and culture be internal strengths or weaknesses? Justify your answer by examples from real market. (
1Mark)
✓
Question 4:
When does a corporation need a board of directors? Justify your answer by an example from Saudi market.
(1 Mark)
Notes:
-
Your answers
(for the
4
questions)
MUST include at least
three scholarly peer-reviewed references
,
using a proper referencing style (APA).
Keep in mind that these scholarly references
can be found
in the
Saudi Digital Library (SDL).
-
Make sure to support your statements with logic and argument, citing all sources referenced.
Your answers should not include m
.
● What are some of the reasons that a MNE would choose internationa.docxanhlodge
● What are some of the reasons that a MNE would choose international expansion through an acquisition? An IJV? An alliance?
● What are the variables that would influence the decision?
● Which choice do you believe is best for the likely benefit of the firm? (Cite and reference).
.
▶︎ Prompt 1 Think about whether you identify with either Blue or .docxanhlodge
▶︎ Prompt 1:
Think about whether you identify with either Blue or Red or "Left vs. Right" characteristics of conservative or liberal, left or right America. Do you see yourself, or the people in the place you grew up, on either side of the divide, or perhaps in a different political category? Share some ways in which you identify with some of the descriptions, or ways in which they seem foreign to you.
I'll attach the picture below
.
⁞ InstructionsChoose only ONE of the following options .docxanhlodge
⁞ Instructions
Choose only
ONE
of the following options below and, in your post, write a paraphrase that avoids plagiarism of the paragraph you have chosen. Your paraphrase can be as long as the excerpt you have chosen, but should not duplicate any phrasing from the excerpt. If you must, you can quote up to three words in a phrase.
Choose to paraphrase ONE of the excerpts below:
Option 1
Morrison began writing Sula in 1969, a time of great activism among African Americans and others who were working toward equal civil rights and opportunities. The book addresses issues of racism, bigotry, and suppression of African Americans; it depicts the despair people feel when they can't get decent jobs, and the determination of some to survive. Eva, for example, cuts off her leg in order to get money to raise her family. Morrison shows how, faced with racist situations, some people had to grovel to whites simply to get by, as Helene does on a train heading through the South. Others, however, fought back, as Sula does when she threatens some white boys who are harassing her and Nel.
or
Option 2
In 1993, Morrison was awarded the Nobel Prize for literature, and thus became the first African American and only the eighth woman ever to win the award. According to Maureen O'Brien in Publishers Weekly, Morrison said, "What is most wonderful for me personally is to know that the Prize has at last been awarded to an African American. I thank God that my mother is alive to see this day." In 1996, she received the National Book Foundation Medal for Distinguished Contribution to American Letters.
.
⁞ InstructionsChoose only ONE of the following options below.docxanhlodge
⁞ Instructions
Choose only
ONE
of the following options below and, in your post, write a paraphrase that avoids plagiarism of the paragraph you have chosen. Your paraphrase can be as long as the excerpt you have chosen, but should not duplicate any phrasing from the excerpt. If you must, you can quote up to three words in a phrase.
When you are done posting your paraphrase, reply to at least one classmate’s paraphrase, commenting on what s/he has done well and what s/he can improve with the wording. Your response should be written in no fewer than 75 words.
Choose to paraphrase ONE of the excerpts below:
Option 1
Morrison began writing Sula in 1969, a time of great activism among African Americans and others who were working toward equal civil rights and opportunities. The book addresses issues of racism, bigotry, and suppression of African Americans; it depicts the despair people feel when they can't get decent jobs, and the determination of some to survive. Eva, for example, cuts off her leg in order to get money to raise her family. Morrison shows how, faced with racist situations, some people had to grovel to whites simply to get by, as Helene does on a train heading through the South. Others, however, fought back, as Sula does when she threatens some white boys who are harassing her and Nel.
or
Option 2
In 1993, Morrison was awarded the Nobel Prize for literature, and thus became the first African American and only the eighth woman ever to win the award. According to Maureen O'Brien in Publishers Weekly, Morrison said, "What is most wonderful for me personally is to know that the Prize has at last been awarded to an African American. I thank God that my mother is alive to see this day." In 1996, she received the National Book Foundation Medal for Distinguished Contribution to American Letters.
Your discussion post will be graded according to the following criteria:
- Clear paraphrase the selected text in your own words with minimal use of quotations
.
⁞ InstructionsAfter reading The Metamorphosis by Frank .docxanhlodge
⁞ Instructions
After reading
The Metamorphosis
by Frank Kafka , choose
one
of the following assertions and write a 200-word response supporting why you agree or disagree with it.
Gregor’s transformation highlights his isolation and alienation before his metamorphosis.
Or
Despite having become an insect, Gregor is more humane and sensitive than his family.
Or
If Gregor had been a stronger person, he would have been able to avoid all of the suffering and alienation he endures.
.
⁞ InstructionsAfter reading all of Chapter 5, please se.docxanhlodge
⁞ Instructions:
After reading all of
Chapter 5
, please select
ONE
of the following
primary source readings
:
“Utilitarianism” by John Stuart Mill
(starting on page 111)
-or-
“A Theory of Justice” by John Rawls
(starting on page 115)
-or-
“The Entitlement Theory of Justice” by Robert Nozick
(starting on page 122)
Write a short, objective summary of
250-500 words
which summarizes the main ideas being put forward by the author in this selection. Your summary should include no direct quotations from any author. Instead, summarize in your own words, and include a citation to the original. Format your Reading Summary assignment according to either MLA or APA formatting standards, and attach as either a .doc, .docx, or .rtf filetype. Other filetypes, or assignments that are merely copy/pasted into the box will be returned ungraded.
.
⁞ InstructionsAfter reading all of Chapter 2, please select.docxanhlodge
⁞ Instructions:
After reading all of
Chapter 2
, please select
ONE
of the following
primary source readings
:
“Anthropology and the Abnormal” by Ruth Benedict
(starting on page 33)
-or-
“Trying Out One’s New Sword” by Mary Midgley
(starting on page 35)
Write a short, objective summary of
250
which summarizes the main ideas being put forward by the author in this selection.
Write a short summary that identifies the thesis and outlines the main argument.
Reading summaries are not about your opinion or perspective – they are expository essays that explain the content of the reading.
All reading summaries must include substantive content based on the students reading of the material.
Reading Material: Doing Ethics
ORIGINIAL WORK. NO PLAGIARISM
.
⁞ Instructions After reading all of Chapter 9, please .docxanhlodge
⁞ Instructions:
After reading all of
Chapter 9
, please select the following
primary source reading
:
“A Defense of Abortion” by Judith Jarvis Thomson
(starting on page 237)
Write a short, objective summary of
250-500 words
which summarizes the main ideas being put forward by the author in this selection. Your summary should include no direct quotations from any author. Instead, summarize in your own words, and include a citation to the original. Format your Reading Summary assignment according to either MLA or APA formatting standards, and attach as either a .doc, .docx, or .rtf filetype. Other filetypes, or assignments that are merely copy/pasted into the box will be returned ungraded.
.
…Multiple intelligences describe an individual’s strengths or capac.docxanhlodge
“…Multiple intelligences describe an individual’s strengths or capacities; learning styles describe an individual’s traits that relate to where and how one best learns” (textbook quote, [H2] Learning Styles].
This week you’ve read about the importance of getting to know your students in order to create relevant and engaging lesson plans that cater to multiple intelligences and are multimodal.
Assignment Instructions:
A. Using
SurveyMonkey
, create a survey that has:
At least five questions based on Gardner’s theory
Five questions on individual learning style inventory
A specific targeted student population grade level (elementary/ middle/ high school/adults)
Include the survey link for your peers
B. Post a minimum 150 word introduction to your survey, using at least one research-based article (cited in APA format) explaining how it will:
Evaluate students’ readiness
Assist in the creation of differentiated lesson plans.
.
••• JONATHAN LETHEM CRITICS OFTEN USE the word prolifi.docxanhlodge
- Jonathan Lethem is known for publishing many novels, stories, essays and other works across different genres. He is described as a "protean" or shape-shifting writer.
- Lethem believes creativity comes from influence and interaction with other works, not isolated originality. He celebrates the "ecstasy of influence" where culture is built upon what came before through borrowing and remixing.
- Many artists, including musicians, visual artists and writers, engage in practices that borrow and reuse elements from other works but these practices are seen as essential to creativity rather than plagiarism. Appropriation and remixing are at the core of cultural production.
•••••iA National Profile ofthe Real Estate Industry and.docxanhlodge
•••••i
A National Profile of
the Real Estate Industry and
the Appraisal Profession
by J. Reid Cummings and Donald R. Epley, PhD, MAI, SRA
FEATURES
T
J- he
he real estate industry has been devastated on many fronts' in the years
following the Great Recession, whieh began in 2007^ due to the bursting of the
housing bubble and the subsequent finaneial crisis relating to the mortgage
market meltdown.' The implosion of the mortgage markets initially began when
two Bear Stearns mortgage-backed securities hedge funds, holding nearly $10
billion in assets, disintegrated into nothing.* Panie quickly spread to financial
institutions that could not hide the extent of their toxic, subprime exposures, and
a massive, worldwide credit squeeze ensued; outright fear soon replaced panic.
Subsequent eredit tightening and substantial illiquidity in the financial markets
rapidly and severely affected the housing and construction markets.' Throughout
the United States, properties of all kinds saw dramatic value declines.
In thousands of cases, real estate foreclosures disrupted people's lives,
forced businesses to close, eaused financial institutions to falter, capsized wbole
market segments, devastated entire industries, and squeezed municipal and state
government budgets dependent upon use and property tax revenues.* While the
effeets of property value declines and the waves of foreclosures in markets across
the country captured most of the headlines, one significant impact of the upheaval
in US real estate markets has gone largely unreported: its impact on employment
in the real estate industry, and specifically, the real estate appraisal profession.
This article presents a
current employment
profile of the US real
estate industry, with
special attention given
to appraisal profes-
sionals. It serves as an
informative picture of
the appraisal profession
for use as a benchmark
for future assessment
of growth. As a
component of the real
estate industry, the
appraisal profession
ranks as the smallest
in employment, is
highly correlated to
movements in empioy-
ment of brokers and
agents, and relies on
commerciai banking,
credit, and real estate
lessors and managers
to deliver its products.
1. James R. DeLisle, "At the Crossroads of Expansion and Recession," TheAppraisalJournal 75, no. 4 (Fall 2007):
314-322; James R. DeLisle, "The Perfect Storm Rippiing Over to Reai Estate," The Appraisal Journal 76, no,
3 (Summer 2008): 200-210.
2. Randaii W. Eberts, "When Wiii US Empioyment Recover from tiie Great Recession?" International Labor Brief
9, no. 2 (2011): 4-12 (W. E. Upjohn Institute for Employment Research): Chad R. Wilkerson, "Recession and
Recovery Across the Nation: Lessons from History," Economic Review 94, no. 2 (2009): 5-24.
3. Kataiina M. Bianco, The Subprime Lending Crisis: Causes and Effects of the Mortgage Meltdown (New York:
CCH, inc., 2008): Lawrence H. White, "Fédérai Reserve Policy and the Housing Bubbie," in Lessons Fro.
Let us consider […] a pair of cases which I shall call Rescue .docxanhlodge
“Let us consider […] a pair of cases which I shall call Rescue I and Rescue II. In the first Rescue story we are hurrying in our jeep to save some people – let there be five of them – who are imminently threatened by the ocean tide. We have not a moment to spare, so when we hear of a single person who also needs rescuing from some other disaster we say regretfully that we cannot rescue him, but must leave him to die. To most of us, this seems clear […]. This is Rescue I and with it I contrast Rescue II. In this second story we are again hurrying to the place where the tide is coming in in order to rescue the party of people, but this time it is relevant that the road is narrow and rocky. In this version, the lone individual is trapped (do not ask me how) on the path. If we are to rescue the five we would have to drive over him. But can we do so? If we stop he will be all right eventually: he is in no danger unless from us. But of course, all five of the others will be drowned. As in the first story, our choice is between a course of action that will leave one man dead and five alive at the end of the day and a course of action which will have the opposite result. (Philippa Foot, “Killing and Letting Die,” from Abortion and Legal Perspectives, eds. Garfield and Hennessey, 2004, University of Massachusetts Press)
1. What would Mill tell the rescuer to do, in Rescue I and Rescue II, according to his theory of utilitarianism? Be clear in explaining Mill’s recommendation, and how he would justify it. In doing so, you must include a discussion of the following:
o The Principle of Utility and how it would specifically apply in this situation—who gets “counted” and how?
2. What would Kant tell the rescuer to do, in Rescue I and Rescue II, according to his deontological theory? Be clear in explaining Kant’s recommendation and how he would justify it. In doing so, you must include a discussion of the following:
o The first version of the Categorical Imperative and how it would specifically apply in these two situations (hint, you have to say what the maxim would be and what duty would be generated according to it).
o The second version of the Categorical Imperative and how it would specifically apply in this situation.
3. Explain one criticism of both Mill and Kant. Afterward, argue for which ethical approach, on your view is superior. Be specific and provide reasons for your claim.
.
• Enhanced eText—Keeps students engaged in learning on th.docxanhlodge
• Enhanced eText—Keeps students engaged in learning on their own time,
while helping them achieve greater conceptual understanding of course
material. The worked examples bring learning to life, and algorithmic practice
allows students to apply the very concepts they are reading about. Combining
resources that illuminate content with accessible self-assessment, MyLab
with Enhanced eText provides students with a complete digital learning
experience—all in one place.
• MediaShare for Business—Consisting of a curated collection of business
videos tagged to learning outcomes and customizable, auto-scored
assignments, MediaShare for Business helps students understand why they
are learning key concepts and how they will apply those in their careers.
Instructors can also assign favorite YouTube clips or original content and
employ MediaShare’s powerful repository of tools to maximize student
accountability and interactive learning, and provide contextualized feedback
for students and teams who upload presentations, media, or business plans.
• Writing Space—Better writers make great
learners who perform better in their courses.
Designed to help you develop and assess concept
mastery and critical thinking, the Writing Space
offers a single place to create, track, and grade
writing assignments, provide resources, and
exchange meaningful, personalized feedback with
students, quickly and easily. Thanks to auto-graded, assisted-graded, and create-your-own assignments, you
decide your level of involvement in evaluating students’ work. The auto-graded option allows you to assign
writing in large classes without having to grade essays by hand. And because of integration with Turnitin®,
Writing Space can check students’ work for improper citation or plagiarism.
• Branching, Decision-Making Simulations—Put your students in the
role of manager as they make a series of decisions based on a realistic
business challenge. The simulations change and branch based on their
decisions, creating various scenario paths. At the end of each simulation,
students receive a grade and a detailed report of the choices they made
with the associated consequences included.
Engage, Assess, Apply
• Learning Catalytics™—Is an interactive, student response tool that
uses students’ smartphones, tablets, or laptops to engage them in
more sophisticated tasks and thinking. Now included with MyLab
with eText, Learning Catalytics enables you to generate classroom
discussion, guide your lecture, and promote peer-to-peer learning
with real-time analytics.
• LMS Integration—You can now link from Blackboard Learn, Brightspace
by D2L, Canvas, or Moodle to MyManagementLab. Access assignments,
rosters, and resources, and synchronize grades with your LMS gradebook.
For students, single sign-on provides access to all the personalized
learning resources that make studying more efficient and effective.
• Reporting Dashboard—View, analyze, and re.
• Here’s the approach you can take for this paperTitle.docxanhlodge
This document outlines the structure for a 15-20 page paper on risk management for an organization. It should include an introduction providing background on the selected organization, descriptions of 3 risks with their impacts and recommendations for managing each risk, a conclusion, and references. The paper needs a title page and should follow APA style formatting.
•Your team will select a big data analytics project that is intr.docxanhlodge
•Your team will select a big data analytics project that is introduced to an organization of your choice … please address the following items:
•Provide a background of the company chosen.
•Determine the problems or opportunities that that this project will solve. What is the value of the project?
•Describe the impact of the problem. In other words, is the organization suffering financial losses? Are there opportunities that are not exploited?
•Provide a clear description regarding the metrics your team will use to measure performance. Please include a discussion pertaining to the key performance indicators (KPIs).
•Recommend a big data tool that will help you solve your problem or exploit the opportunity, such as Hadoop, Cloudera, MongoDB, or Hive.
•Evaluate the data requirements. Here are questions to consider: What type of data is needed? Where can you find the data? How can the data be collected? How can you verify the integrity of the data?
•Discuss the gaps that you will need to bridge. Will you need help from vendors to do this work? Is it necessary to secure the services of other subject matter experts (SMEs)?
•What type of project management approach will you use this initiative? Agile? Waterfall? Hybrid? Please provide a justification for the selected approach.
•Provide a summary and conclusion.
.
Temple of Asclepius in Thrace. Excavation resultsKrassimira Luka
The temple and the sanctuary around were dedicated to Asklepios Zmidrenus. This name has been known since 1875 when an inscription dedicated to him was discovered in Rome. The inscription is dated in 227 AD and was left by soldiers originating from the city of Philippopolis (modern Plovdiv).
Chapter wise All Notes of First year Basic Civil Engineering.pptxDenish Jangid
Chapter wise All Notes of First year Basic Civil Engineering
Syllabus
Chapter-1
Introduction to objective, scope and outcome the subject
Chapter 2
Introduction: Scope and Specialization of Civil Engineering, Role of civil Engineer in Society, Impact of infrastructural development on economy of country.
Chapter 3
Surveying: Object Principles & Types of Surveying; Site Plans, Plans & Maps; Scales & Unit of different Measurements.
Linear Measurements: Instruments used. Linear Measurement by Tape, Ranging out Survey Lines and overcoming Obstructions; Measurements on sloping ground; Tape corrections, conventional symbols. Angular Measurements: Instruments used; Introduction to Compass Surveying, Bearings and Longitude & Latitude of a Line, Introduction to total station.
Levelling: Instrument used Object of levelling, Methods of levelling in brief, and Contour maps.
Chapter 4
Buildings: Selection of site for Buildings, Layout of Building Plan, Types of buildings, Plinth area, carpet area, floor space index, Introduction to building byelaws, concept of sun light & ventilation. Components of Buildings & their functions, Basic concept of R.C.C., Introduction to types of foundation
Chapter 5
Transportation: Introduction to Transportation Engineering; Traffic and Road Safety: Types and Characteristics of Various Modes of Transportation; Various Road Traffic Signs, Causes of Accidents and Road Safety Measures.
Chapter 6
Environmental Engineering: Environmental Pollution, Environmental Acts and Regulations, Functional Concepts of Ecology, Basics of Species, Biodiversity, Ecosystem, Hydrological Cycle; Chemical Cycles: Carbon, Nitrogen & Phosphorus; Energy Flow in Ecosystems.
Water Pollution: Water Quality standards, Introduction to Treatment & Disposal of Waste Water. Reuse and Saving of Water, Rain Water Harvesting. Solid Waste Management: Classification of Solid Waste, Collection, Transportation and Disposal of Solid. Recycling of Solid Waste: Energy Recovery, Sanitary Landfill, On-Site Sanitation. Air & Noise Pollution: Primary and Secondary air pollutants, Harmful effects of Air Pollution, Control of Air Pollution. . Noise Pollution Harmful Effects of noise pollution, control of noise pollution, Global warming & Climate Change, Ozone depletion, Greenhouse effect
Text Books:
1. Palancharmy, Basic Civil Engineering, McGraw Hill publishers.
2. Satheesh Gopi, Basic Civil Engineering, Pearson Publishers.
3. Ketki Rangwala Dalal, Essentials of Civil Engineering, Charotar Publishing House.
4. BCP, Surveying volume 1
Level 3 NCEA - NZ: A Nation In the Making 1872 - 1900 SML.pptHenry Hollis
The History of NZ 1870-1900.
Making of a Nation.
From the NZ Wars to Liberals,
Richard Seddon, George Grey,
Social Laboratory, New Zealand,
Confiscations, Kotahitanga, Kingitanga, Parliament, Suffrage, Repudiation, Economic Change, Agriculture, Gold Mining, Timber, Flax, Sheep, Dairying,
How to Setup Warehouse & Location in Odoo 17 InventoryCeline George
In this slide, we'll explore how to set up warehouses and locations in Odoo 17 Inventory. This will help us manage our stock effectively, track inventory levels, and streamline warehouse operations.
A Visual Guide to 1 Samuel | A Tale of Two HeartsSteve Thomason
These slides walk through the story of 1 Samuel. Samuel is the last judge of Israel. The people reject God and want a king. Saul is anointed as the first king, but he is not a good king. David, the shepherd boy is anointed and Saul is envious of him. David shows honor while Saul continues to self destruct.
How to Make a Field Mandatory in Odoo 17Celine George
In Odoo, making a field required can be done through both Python code and XML views. When you set the required attribute to True in Python code, it makes the field required across all views where it's used. Conversely, when you set the required attribute in XML views, it makes the field required only in the context of that particular view.
ISO/IEC 27001, ISO/IEC 42001, and GDPR: Best Practices for Implementation and...PECB
Denis is a dynamic and results-driven Chief Information Officer (CIO) with a distinguished career spanning information systems analysis and technical project management. With a proven track record of spearheading the design and delivery of cutting-edge Information Management solutions, he has consistently elevated business operations, streamlined reporting functions, and maximized process efficiency.
Certified as an ISO/IEC 27001: Information Security Management Systems (ISMS) Lead Implementer, Data Protection Officer, and Cyber Risks Analyst, Denis brings a heightened focus on data security, privacy, and cyber resilience to every endeavor.
His expertise extends across a diverse spectrum of reporting, database, and web development applications, underpinned by an exceptional grasp of data storage and virtualization technologies. His proficiency in application testing, database administration, and data cleansing ensures seamless execution of complex projects.
What sets Denis apart is his comprehensive understanding of Business and Systems Analysis technologies, honed through involvement in all phases of the Software Development Lifecycle (SDLC). From meticulous requirements gathering to precise analysis, innovative design, rigorous development, thorough testing, and successful implementation, he has consistently delivered exceptional results.
Throughout his career, he has taken on multifaceted roles, from leading technical project management teams to owning solutions that drive operational excellence. His conscientious and proactive approach is unwavering, whether he is working independently or collaboratively within a team. His ability to connect with colleagues on a personal level underscores his commitment to fostering a harmonious and productive workplace environment.
Date: May 29, 2024
Tags: Information Security, ISO/IEC 27001, ISO/IEC 42001, Artificial Intelligence, GDPR
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ISO/IEC 27001, ISO/IEC 42001, and GDPR: Best Practices for Implementation and...
SAMPLING MEANDEFINITIONThe term sampling mean is a stati.docx
1. SAMPLING MEAN:
DEFINITION:
The term sampling mean is a statistical term used to describe
the properties of statistical distributions. In statistical terms, the
sample meanfrom a group of observations is an estimate of the
population mean. Given a sample of size n, consider n
independent random variables X1, X2... Xn, each corresponding
to one randomly selected observation. Each of these variables
has the distribution of the population, with mean and standard
deviation. The sample mean is defined to be
WHAT IT IS USED FOR:
It is also used to measure central tendency of the numbers in a
database. It can also be said that it is nothing more than a
balance point between the number and the low numbers.
HOW TO CALCULATE IT:
To calculate this, just add up all the numbers, then divide by
how many numbers there are.
Example: what is the mean of 2, 7, and 9?
Add the numbers: 2 + 7 + 9 = 18
Divide by how many numbers (i.e., we added 3 numbers): 18 ÷
3 = 6
So the Mean is 6
2. SAMPLE VARIANCE:
DEFINITION:
The sample variance, s2, is used to calculate how varied a
sample is. A sample is a select number of items taken from a
population. For example, if you are measuring American
people’s weights, it wouldn’t be feasible (from either a time or
a monetary standpoint) for you to measure the weights of every
person in the population. The solution is to take a sample of the
population, say 1000 people, and use that sample size to
estimate the actual weights of the whole population.
WHAT IT IS USED FOR:
The sample variance helps you to figure out the spread out in
the data you have collected or are going to analyze. In
statistical terminology, it can be defined as the average of the
squared differences from the mean.
HOW TO CALCULATE IT:
Given below are steps of how a sample variance is calculated:
· Determine the mean
· Then for each number: subtract the Mean and square the result
· Then work out the mean of those squared differences.
To work out the mean, add up all the values then divide by the
number of data points.
First add up all the values from the previous step.
But how do we say "add them all up" in mathematics? We use
3. the Roman letter Sigma: Σ
The handy Sigma Notation says to sum up as many terms as we
want.
· Next we need to divide by the number of data points, which is
simply done by multiplying by "1/N":
Statistically it can be stated by the following:
·
· This value is the variance
EXAMPLE:
Sam has 20 Rose Bushes.
The number of flowers on each bush is
9, 2, 5, 4, 12, 7, 8, 11, 9, 3, 7, 4, 12, 5, 4, 10, 9, 6, 9, 4
Work out the sample variance
Step 1. Work out the mean
In the formula above, μ (the Greek letter "mu") is the mean of
all our values.
For this example, the data points are: 9, 2, 5, 4, 12, 7, 8, 11, 9,
3, 7, 4, 12, 5, 4, 10, 9, 6, 9, 4
The mean is:
(9+2+5+4+12+7+8+11+9+3+7+4+12+5+4+10+9+6+9+4) / 20 =
140/20 = 7
So:
μ = 7
Step 2. Then for each number: subtract the Mean and square the
result
This is the part of the formula that says:
So what is xi? They are the individual x values 9, 2, 5, 4, 12, 7,
etc...
In other words x1 = 9, x2 = 2, x3 = 5, etc.
So it says "for each value, subtract the mean and square the
4. result", like this
Example (continued):
(9 - 7)2 = (2)2 = 4
(2 - 7)2 = (-5)2 = 25
(5 - 7)2 = (-2)2 = 4
(4 - 7)2 = (-3)2 = 9
(12 - 7)2 = (5)2 = 25
(7 - 7)2 = (0)2 = 0
(8 - 7)2 = (1)2 = 1
We need to do this for all the numbers
Step 3. Then work out the mean of those squared differences.
To work out the mean, add up all the values then divide by how
many.
First add up all the values from the previous step.
= 4+25+4+9+25+0+1+16+4+16+0+9+25+4+9+9+4+1+4+9 = 178
But that isn't the mean yet, we need to divide by how many,
which is simply done by multiplying by "1/N":
Mean of squared differences = (1/20) × 178 = 8.9
This value is called the variance.
STANDARD DEVIAITON:
DEFINITION:
This descriptor shows how much variation or dispersion from
the average exists.
The symbol for Standard Deviation is σ (the Greek letter
sigma).
It is calculated using:
In case of a sample the ‘N’ in this formula is replaced by n-1.
5. WHAT IT IS USED FOR:
It is used to determine the expected value. A low standard
deviation indicates that the data points tend to be very close to
the mean (also called expected value); a high standard deviation
indicates that the data points are spread out over a large range
of values.
HOW TO CALCULATE IT:
To determine the standard deviation, you need to take the
square root of the variance.
EXAMPLE PROBLEM:
Let’s look at the previous problem and compute the standard
deviation. The standard deviation as mentioned earlier is
nothing more than the measure of dispersion (spread). It can be
calculated by taking the square root of the variance. In case of
the previous problem where the variance was 8.9, its
corresponding standard deviation would be the square root of
8.9 which is 2.983
σ = √(8.9) = 2.983...
HYPOTHESES TESTING:
DEFINITION:
Hypothesis testing is a topic at the heart of statistics. This
technique belongs to a realm known as inferential statistics.
Researchers from all sorts of different areas, such as
psychology, marketing, and medicine, formulate hypotheses or
claims about a population being studied.
WHAT IT IS USED FOR:
6. Hypothesis testing is used to determine the validity of these
claims. Carefully designed statistical experiments obtain sample
data from the population. The data is in turn used to test the
accuracy of a hypothesis concerning a population. Hypothesis
tests are based upon the field of mathematics known as
probability. Probability gives us a way to quantify how likely it
is for an event to occur. The underlying assumption for all
inferential statistics deals with rare events, which is why
probability is used so extensively. The rare event rule states
that if an assumption is made and the probability of a certain
observed event is very small, then the assumption is most likely
incorrect.
The basic idea here is that we test a claim by distinguishing
between two different things:
1. An event that easily occurs by chance
2. An event that is highly unlikely to occur by chance.
If a highly unlikely event occurs, then we explain this by stating
that a rare event really did take place, or that the assumption we
started with was not true.
HOW TO USE THE TEST FOR DECISION MAKING
PURPOSES:
1. Formulate the null hypothesis(commonly, that the
observations are the result of pure chance) and the alternative
hypothesis(commonly, that the observations show a real effect
combined with a component of chance variation).
2. Identify a test statistic that can be used to assess the truth of
the null hypothesis.
3. Compute the P-value, which is the probability that a test
statistic at least as significant as the one observed would be
obtained assuming that the null hypothesis were true. The
smaller the -value, the stronger the evidence against the null
hypothesis.
4. Compare the -value to an acceptable significance value
(sometimes called an alpha value). If , that the observed effect
is statistically significant, the null hypothesis is ruled out, and
7. the alternative hypothesis is valid.
EXAMPLE OF HYPOTHESIS TESTING (TWO-TAIL TEST)
If you are told that the mean weight of 3rd graders is 85 pounds
with a standard deviation of 20 pounds, and you find that the
mean weight of a group of 22 students is 95 pounds, do you
question that that group of students is a group of third graders?
· The z-score is ((x-bar) - µ)/(*sigma*/(n^.5)); the numerator is
the difference between the observed and hypothesized mean, the
denominator rescales the unit of measurement to standard
deviation units. (95-85)/(20/(22^.5)) = 2.3452.
· The z-score 2.35 corresponds to the probability .9906, which
leaves .0094 in the tail beyond. Since one could have been as
far below 85, the probability of such a large or larger z-score is
.0188. This is the p-value. Note that for these two tailed tests
we are using the absolute value of the z-score.
· Because .0188 < .05, we reject the hypothesis (which we shall
call the null hypothesis) at the 5% significance level; if the null
hypothesis were true, we would get such a large z-score less
than 5% of the time. Because .0188 > .01, we fail to reject the
null hypothesis at the 1% level; if the null hypothesis were true,
we would get such a large z-score more than 1% of the time.
DECISION TREE:
DEFINITION:
A schematic tree-shaped diagram used to determine a course of
action or show a statistical probability. Each branch of the
decision tree represents a possible decision or occurrence. The
tree structure shows how one choice leads to the next, and the
use of branches indicates that each option is mutually exclusive.
WHAT IT IS USED FOR:
A decision tree can be used to clarify and find an answer to a
complex problem. The structure allows users to take a problem
with multiple possible solutions and display it in a simple, easy-
to-understand format that shows the relationship between
8. different events or decisions. The furthest branches on the tree
represent possible end results.
HOW TO APPLY IT:
1. As a starting point for the decision tree, draw a small square
around the center of the left side of the paper. If the description
is too large to fit the square, use legends by including a number
in the tree and referencing the number to the description either
at the bottom of the page or in another page.
2. Draw out lines (forks) to the right of the square box. Draw
one line each for each possible solution to the issue, and
describe the solution along the line. Keep the lines as far apart
as possible to expand the tree later.
3. Illustrate the results or the outcomes of the solution at the
end of each line. If the outcome is uncertain, draw a circle
(chance node). If the outcome leads to another issue, draw a
square (decision node). If the issue is resolved with the
solution, draw a triangle (end node). Describe the outcome
above the square or circle, or use legends, as appropriate.
4. Repeat steps 2 through 4 for each new square at the end of
the solution lines, and so on until there are no more squares,
and all lines have either a circle or blank ending.
5. The circles that represent uncertainty remain as they are. A
good practice is to assign a probability value, or the chance of
such an outcome happening.
Since it is difficult to predict at onset the number of lines and
sub-lines each solution generates, the decision tree might
require one or more redraws, owing to paucity of space to
illustrate or represent options and/or sub-options at certain
spaces.
It is a good idea to challenge and review all squares and circles
for possible overlooked solutions before finalizing the draft.
EXAMPLE:
Your company is considering whether it should tender for two
contracts (MS1 and MS2) on offer from a government
department for the supply of certain components. The company
has three options:
9. · tender for MS1 only; or
· tender for MS2 only; or
· tender for both MS1 and MS2.
If tenders are to be submitted, the company will incur additional
costs. These costs will have to be entirely recouped from the
contract price. The risk, of course, is that if a tender is
unsuccessful, the company will have made a loss.
The cost of tendering for contract MS1 only is $50,000. The
component supply cost if the tender is successful would be
$18,000.
The cost of tendering for contract MS2 only is $14,000. The
component supply cost if the tender is successful would be
$12,000.
The cost of tendering for both contracts MS1 and MS2 is
$55,000. The component supply cost if the tender is successful
would be $24,000.
For each contract, possible tender prices have been determined.
In addition, subjective assessments have been made of the
probability of getting the contract with a particular tender price
as shown below. Note here that the company can only submit
one tender and cannot, for example, submit two tenders (at
different prices) for the same contract.
Option Possible Probability
tender of getting
prices ($)contract
MS1 only 130,000 0.20
115,000 0.85
MS2 only 70,000 0.15
65,000 0.80
60,000 0.95
MS1 and MS2 190,000 0.05
140,000 0.65
In the event that the company tenders for both MS1 and MS2 it
10. will either win both contracts (at the price shown above) or no
contract at all.
· What do you suggest the company should do and why?
· What are the downside and the upside of your suggested
course of action?
· A consultant has approached your company with an offer that
in return for $20,000 in cash, she will ensure that if you tender
$60,000 for contract MS2, only your tender is guaranteed to be
successful. Should you accept her offer or not and why?
Solution
The decision tree for the problem is shown below.
Below we carry out step 1 of the decision tree solution
procedure which (for this example) involves working out the
total profit for each of the paths from the initial node to the
terminal node (all figures in $'000).
Step 1
· path to terminal node 12, we tender for MS1 only (cost 50), at
a price of 130, and win the contract, so incurring component
supply costs of 18, total profit 130-50-18 = 62
· path to terminal node 13, we tender for MS1 only (cost 50), at
a price of 130, and lose the contract, total profit -50
· path to terminal node 14, we tender for MS1 only (cost 50), at
11. a price of 115, and win the contract, so incurring component
supply costs of 18, total profit 115-50-18 = 47
· path to terminal node 15, we tender for MS1 only (cost 50), at
a price of 115, and lose the contract, total profit -50
· path to terminal node 16, we tender for MS2 only (cost 14), at
a price of 70, and win the contract, so incurring component
supply costs of 12, total profit 70-14-12 = 44
· path to terminal node 17, we tender for MS2 only (cost 14), at
a price of 70, and lose the contract, total profit -14
· path to terminal node 18, we tender for MS2 only (cost 14), at
a price of 65, and win the contract, so incurring component
supply costs of 12, total profit 65-14-12 = 39
· path to terminal node 19, we tender for MS2 only (cost 14), at
a price of 65, and lose the contract, total profit -14
· path to terminal node 20, we tender for MS2 only (cost 14), at
a price of 60, and win the contract, so incurring component
supply costs of 12, total profit 60-14-12 = 34
· path to terminal node 21, we tender for MS2 only (cost 14), at
a price of 60, and lose the contract, total profit -14
· path to terminal node 22, we tender for MS1 and MS2 (cost
55), at a price of 190, and win the contract, so incurring
component supply costs of 24, total profit 190-55- 24=111
· path to terminal node 23, we tender for MS1 and MS2 (cost
55), at a price of 190, and lose the contract, total profit -55
· path to terminal node 24, we tender for MS1 and MS2 (cost
12. 55), at a price of 140, and win the contract, so incurring
component supply costs of 24, total profit 140-55- 24=61
· path to terminal node 25, we tender for MS1 and MS2 (cost
55), at a price of 140, and lose the contract, total profit -55
Hence we can arrive at the table below indicating for each
branch the total profit involved in that branch from the initial
node to the terminal node.
Terminal node Total profit $'000
12 62
13 -50
14 47
15 -50
16 44
17 -14
18 39
19 -14
20 34
21 -14
22 111
23 -55
24 61
25 -55
We can now carry out the second step of the decision tree
solution procedure where we work from the right-hand side of
the diagram back to the left-hand side.
13. Step 2
· For chance node 5 the EMV is 0.2(62) + 0.8(-50) = -27.6
· For chance node 6 the EMV is 0.85(47) + 0.15(-50) = 32.45
Hence the best decision at decision node 2 is to tender at a price
of 115 (EMV=32.45).
· For chance node 7 the EMV is 0.15(44) + 0.85(-14) = -5.3
· For chance node 8 the EMV is 0.80(39) + 0.20(-14) = 28.4
· For chance node 9 the EMV is 0.95(34) + 0.05(-14) = 31.6
Hence the best decision at decision node 3 is to tender at a price
of 60 (EMV=31.6).
· For chance node 10 the EMV is 0.05(111) + 0.95(-55) = -46.7
· For chance node 11 the EMV is 0.65(61) + 0.35(-55) = 20.4
Hence the best decision at decision node 4 is to tender at a price
of 140 (EMV=20.4).
Hence at decision node 1 we have three alternatives:
· tender for MS1 only EMV=32.45
· tender for MS2 only EMV=31.6
· tender for both MS1 and MS2 EMV = 20.4
Hence the best decision is to tender for MS1 only (at a price of
115) as it has the highest expected monetary value of 32.45
($'000).
INFLUENCE OF SAMPLE SIZE:
DEFINITION:
Sample size is one of the four interrelated features of a study
14. design that can influence the detection of significant
differences, relationships, or interactions. Generally, these
survey designs try to minimize both alpha error (finding a
difference that does not actually exist in the population) and
beta error (failing to find a difference that actually exists in the
population).
WHAT IT IS USED FOR:
The sample size used in a study is determined based on the
expense of data collection and the need to have sufficient
statistical power.
HOW TO USE IT:
We already know that the margin of error is 1.96 times the
standard error and that the standard error is sq.rt ^p(1�^p)/n. In
general, the formula is ME = z sq.rt ^p(1-^p)/n
where
*ME is the desired margin of error
*z is the z-score, e.g., 1.645 for a 90% confidence interval, 1.96
for a 90% confidence interval, 2.58 for a 99% confidence
interval
_ ^p is our prior judgment of the correct value of p.
15. _ n is the sample size (to be found)
EXAMPLE:
If ^p =0.3 and Z=1.96 and ME =0.025 then the necessary sample
size is:
ME= Z sq.rt (^p*1-^p)/n
0.025 = 1:96 sq.rt (0.3*0.7)/n
n=1291 or 1300 students
POPULATION MEAN:
DEFINITION:
The population mean is the mean of a numerical set that
includes all the numbers within the entire group.
WHAT IT IS USED FOR:
In most cases, the population mean is unknown and the sample
16. mean is used for validation purposes. However, if we want to
calculate the population mean, we will have to construct the
confidence interval. This can be achieved by the following
steps:
HOW TO USE IT:
· The sample statistic is the sample mean x¯
· The standard error of the mean is s/sq.rt n where s is the
standard deviation of individual data values.
· The multiplier, denoted by t*, is found using the t-table in the
appendix of the book. It's a simple table. There are columns for
.90, .95, .98, and .99 confidence. Use the row for df = n − 1.
· Thus the formula for a confidence interval for the mean is
x¯±t∗ (s/sq.rt n)
EXAMPLE:
In a class survey, students are asked if they are sleep deprived
or not and also are asked how much they sleep per night.
Summary statistics for the n = 22 students who said they are
sleep deprived are:
· Thus n = 22, x¯ = 5.77, s = 1.572, and standard error of the
mean = 1.572/sq.rt 22=0.335
· A confidence interval for the mean amount of sleep per night
17. is 5.77 ± t* (0.335) for the population that feels sleep deprived.
· Go to the t-table in the appendix of the book and use the df =
22 – 1 = 21 row. For 95% confidence the value of t* = 2.08.
· A 95% confidence interval for μ is 5.77 ± (2.08) (0.335),
which is 5.77 ± 0.70, or 5.07 to 6.7
· Interpretation: With 95% confidence we estimate the
population mean to be between 5.07 and 6.47 hours per night.
RANDOM SAMPLING
Random sampling is a sampling technique where we select a
group of subjects (a sample) for study from a larger group (a
population). Each individual is chosen entirely by chance and
each member of the population has a known, but possibly non-
equal, chance of being included in the sample.
By using random sampling, the likelihood of bias is reduced.
WHEN RANDOM SAMPLING IS USED:
Random sampling is used when the researcher knows little
about the population.
THE STEPS ASSOCIATED WITH RANDOM SAMPLING:
1. Define the population
2. Choose your sample size
3. List the population
18. 4. Assign numbers to the units
5. Find random numbers
6. Select your sample
EXAMPLE:
In a study, 10,000 students will be invited to take part in the
research study. The selection was limited to 200 randomly
selected students. In this case, this would mean selecting 200
random numbers from the random number table. Imagine the
first three numbers from the random number table were:
0011
(the 11th student from the numbered list of 10,000 students)
9292
(the 9,292nd student from the list)
2001
(the 2,001st student from the list)
We would select the 11th, 9,292nd, and 2,001st students from
our list to be part of the sample. We keep doing this until we
have all 200 students that we want in our sample.
SAMPLING DISTRIBUTION:
DEFINITION:
19. The sampling distribution is a theoretical distribution of a
sample statistic. There is a different sampling distribution for
each sample statistic. Each sampling distribution is
characterized by parameters, two of which are and. The latter is
called the standard error.
WHAT IT IS USED FOR:
It is used for making probability statements in inferential
statistics.
HOW IS SAMPLING DISTRIBUTION USED?
Step 1: Obtain a simple random sample of size n.
Step 2: Compute the sample mean.
Step 3: Assuming we are sampling from a finite population,
repeat Steps 1 and 2 until all simple random samples of size n
have been obtained.
EXAMPLE OF SAMPLING DISTRIBUTION:
THE SAMPLE DISTRIBUTION
The sample distribution is the distribution resulting from the
collection of actual data. A major characteristic of a sample is
that it contains a finite (countable) number of scores, the
number of scores represented by the letter N. For example,
suppose that the following data were collected:
32
35
42
33
21. 32
39
37
35
36
39
33
31
40
37
34
34
37
These numbers constitute a sample distribution. Using the
procedures discussed in the chapter on frequency distributions,
the following relative frequency polygon can be constructed to
picture this data:
SAMPLING ERROR:
DEFINITION:
The error that arises as a result of taking a sample from a
population rather than using the whole population.
WHAT IT IS USED FOR:
It is used to detect the difference between the sample and the
true, but unknown value of population parameter.
22. HOW TO USE IT/CALCULATE IT:
· Determine the level of confidence followed by the critical
values
· Calculate the sample standard deviation
· Calculate the margin of error using
E = Critical value * sample standard deviation/sq.rt of sample
size
EXAMPLE:
1. What is the margin of error for a simple random sample of
900 people at a 95% level of confidence? The sample standard
deviation is 2.
By use of the table we have a critical value of 1.96, and so the
margin of error is 1.96/(2 √ 900 = 0.03267, or about 3.3%.
2. What is the margin of error for a simple random sample of
1600 people at a 95% level of confidence and a sample standard
deviation of 2?
At the same level of confidence as the first example, increasing
the sample size to 1600 gives us a margin of error of 0.0245, or
about 2.5%.
This shows that by increasing the sample size, the margin of
error decreases.
PROBABILITY:
DEFINITION:
23. Probability is the chance that something will happen — how
likely it is that some event will occur.
WHAT IT IS USED FOR:
Probability is used in various areas, such as assessing risks in
medical treatment, forecasting weather, what to sell at a
discount and when to sell it, determining car insurance rates,
determining future commercial and manufacturing construction,
in developing other real estate, in municipal planning for such
things as placing new roads, and in financial planning at home
and in the business world.
HOW TO CALCUATE IT:
1. Count the number of all distinctive and equally likely
outcomes of the experiment. Let that be n.
2. Count the number of distinctive outcomes that represent the
occurrence of the event in question. Let that be ne.
3. Calculate the result of the division ne/n. That is the
probability of the event.
EXAMPLE:
Find the probability of getting an even number after rolling a
die.
24. · Event: Getting an even number
· Steps above:
· Distinctive outcomes: 1, 2, 3, 4, 5, 6 are all the outcomes,
their count n=6
· Outcomes representing the event: 2, 4, 6 are all the even
numbers you can get, their count ne=3
· Probability: P = ne/n = 3/6 = 0.5 or 1/2
POWER CURVE:
DEFINITION:
Power curves illustrate the effect on power of varying the
alternate hypothesis.
WHAT IT IS USED FOR:
The curve illustrates how a sample of observations with a
defined variance is quite powerful in correctly rejecting the null
hypothesis (for example, if m0=8) when the true mean is less
than 6 or greater than 10. The curve also illustrates that the test
is not powerful — it may not reject the null hypothesis even
when the true mean differs from m0 — when the difference is
small. This is also extensively used in testing the relationship
25. between power and sample size.
HOW IT IS USED:
See example below.
EXAMPLE:
If the researcher learns from literature that the population
follows a normal distribution with mean of 100 and variance of
100 under the null hypothesis and he/she expects the mean to be
greater than 105 or less than 95 under the null hypothesis and
he/she wants the test to be significant at 95% level, the
resulting power function would be:
Power=1-Φ[1.96-(105-100)/(10/n)]+Φ[-1.96-(95-100)/(10/n)],
which is,
Power=1-Φ[1.96-n/2]+Φ[-1.96+n/2].
That function shows a relationship between power and sample
size. For each level of sample size, there is a corresponding
sample size. For example, if n=20, the corresponding power
level would be about 0.97, or, if the power level is 0.95, the
corresponding sample size would be 16.
PROBABILITY DISTRIBUTION:
26. DEFINITION:
A statistical function that describes all the possible values and
likelihoods that a random variable can take within a given
range. At times it is presented in the form of a table or an
equation that links the outcome of a statistical experiment with
its probability of occurrences.
HOW IT IS USED:
It establishes a range that will be between the minimum and
maximum statistically possible values, but where the possible
values are likely to be plotted on the probability distribution
depends on a number of factors, including the distribution
mean, standard deviation, skewness, and kurtosis.
HOW TO USE IT:
· Identify the event
· Create a table showing the possibility of its occurrence
EXAMPLE:
An example will make clear the relationship between random
variables and probability distributions. Suppose you flip a coin
27. two times. This simple statistical experiment can have four
possible outcomes: HH, HT, TH, and TT. Now, let the variable
X represent the number of Heads that result from this
experiment. The variable X can take on the values 0, 1, or 2. In
this example, X is a random variable because its value is
determined by the outcome of a statistical experiment.
A probability distribution is a table or an equation that links
each outcome of a statistical experiment with its probability of
occurrence. Consider the coin flip experiment described above.
The table below, which associates each outcome with its
probability, is an example of a probability distribution.
Number of heads
Probability
0
0.25
1
0.50
2
0.25
The above table represents the probability distribution of the
random variable X.
EXPECTED VALUE OF SAMPLE INFORMATION:
DEFINITION:
In decision theory, the expected value of sample information is
28. the expected increase in utility that you could obtain from
gaining access to a sample of additional observations before
making a decision.
WHAT IS IT USED FOR?
Calculate the Expected Monetary Value (EMV) of each
alternative action.
HOW TO USE IT/CALCULATE IT?
1.Determine the optimal decision and its expected return for the
possible outcomes of the sample using the posterior
probabilities for the states of nature
2. Calculate the values of the optimal returns
3.Subtract the EV of the optimal decision obtained without
using the sample information from the amount determined in
step (2)
EXAMPLE:
The expected value of sample information is computed as
follows:
29. Suppose you were going to make an investment into only one of
three investment vehicles: stock, mutual fund, or certificate of
deposit (CD). Further suppose that the market has a 50% chance
of increasing, a 30% chance of staying even, and a 20% chance
of decreasing. If the market increases, the stock investment will
earn $1500 and the mutual fund will earn $900. If the market
stays even, the stock investment will earn $300 and the mutual
fund will earn $600. If the market decreases, the stock
investment will lose $800 and the mutual fund will lose $200.
The certificate of deposit will earn $500 independent of the
market's fluctuation.
Question:
What is the expected value of perfect information?