This document discusses various numerical measures used to describe data, including measures of central tendency (mean, median, mode) and measures of dispersion (range, variance, standard deviation). It provides definitions and formulas for calculating these measures, along with examples of calculating the mean, median, mode, weighted mean, variance, standard deviation, and other concepts. The learning objectives cover explaining central tendency, computing various means, determining the median and mode, calculating the geometric mean, explaining and applying measures of dispersion, computing standard deviation, and concepts like Chebyshev's Theorem and the Empirical Rule.
Business statistics takes the data analysis tools from elementary statistics and applies them to business. For example, estimating the probability of a defect coming off a factory line, or seeing where sales are headed in the future. Many of the tools used in business statistics are built on ones you’ve probably already come across in basic math: mean, mode and median, bar graphs and the bell curve, and basic probability. Hypothesis testing (where you test out an idea) and regression analysis (fitting data to an equation) builds on this foundation.
This document discusses various numerical measures used to describe data, including measures of central tendency (mean, median, mode) and dispersion (range, variance, standard deviation). It provides definitions and formulas for these concepts, as well as examples of computing each measure. The learning objectives cover explaining the concept of central tendency, identifying and computing the mean, median, and mode, calculating the geometric mean, explaining and applying measures of dispersion such as standard deviation, explaining Chebyshev's Theorem and the Empirical Rule, and computing statistics for grouped data.
This document provides an overview of key concepts for describing numerical data, including measures of central tendency (such as the mean, median, mode, weighted mean, and geometric mean) and measures of dispersion (such as the range, mean deviation, variance and standard deviation). It defines each measure and provides examples to demonstrate how to calculate and interpret the measures. The learning objectives cover explaining the concept of central tendency, identifying and computing various measures of central tendency and dispersion, and applying the measures to analyze datasets.
3 goals calculate the arithmetic mean, weighted mean,smile790243
This document discusses various statistical concepts including:
- Measures of central tendency like the mean, median, mode, weighted mean, and geometric mean. It provides definitions and examples of calculating each measure.
- Measures of dispersion like range, mean deviation, variance, and standard deviation. It defines each measure and provides examples of calculating variance and standard deviation.
- Other concepts like Chebyshev's theorem, empirical rule, and how to calculate measures for grouped data. It discusses the characteristics and appropriate uses of central tendency and dispersion measures.
The document provides an overview of statistical concepts including descriptive and inferential statistics, measures of central tendency and dispersion, hypothesis testing procedures, and examples of one-sample and two-sample hypothesis tests. Specifically, it discusses topics such as the mean, median, mode, range, variance, standard deviation, stating hypotheses, identifying test statistics, formulating decision rules, taking samples, and interpreting results. Examples are given to illustrate one-sample t-tests and two-sample z-tests for comparing population means with known and equal variances.
The document provides an overview of PSPP software and statistical analysis techniques, including:
- Descriptive statistics such as measures of central tendency (mean, median, mode), measures of dispersion (range, variance, standard deviation), and data displays (frequency tables, bar charts, pie charts, histograms)
- The difference between descriptive and inferential statistics, and an introduction to hypothesis testing including stating hypotheses, significance levels, test statistics, and decision rules.
- Examples of one-sample and two-sample hypothesis tests, comparing population means when variances are known or unknown, to determine if samples are representative of populations.
Business statistics takes the data analysis tools from elementary statistics and applies them to business. For example, estimating the probability of a defect coming off a factory line, or seeing where sales are headed in the future. Many of the tools used in business statistics are built on ones you’ve probably already come across in basic math: mean, mode and median, bar graphs and the bell curve, and basic probability. Hypothesis testing (where you test out an idea) and regression analysis (fitting data to an equation) builds on this foundation.
This document discusses various numerical measures used to describe data, including measures of central tendency (mean, median, mode) and dispersion (range, variance, standard deviation). It provides definitions and formulas for these concepts, as well as examples of computing each measure. The learning objectives cover explaining the concept of central tendency, identifying and computing the mean, median, and mode, calculating the geometric mean, explaining and applying measures of dispersion such as standard deviation, explaining Chebyshev's Theorem and the Empirical Rule, and computing statistics for grouped data.
This document provides an overview of key concepts for describing numerical data, including measures of central tendency (such as the mean, median, mode, weighted mean, and geometric mean) and measures of dispersion (such as the range, mean deviation, variance and standard deviation). It defines each measure and provides examples to demonstrate how to calculate and interpret the measures. The learning objectives cover explaining the concept of central tendency, identifying and computing various measures of central tendency and dispersion, and applying the measures to analyze datasets.
3 goals calculate the arithmetic mean, weighted mean,smile790243
This document discusses various statistical concepts including:
- Measures of central tendency like the mean, median, mode, weighted mean, and geometric mean. It provides definitions and examples of calculating each measure.
- Measures of dispersion like range, mean deviation, variance, and standard deviation. It defines each measure and provides examples of calculating variance and standard deviation.
- Other concepts like Chebyshev's theorem, empirical rule, and how to calculate measures for grouped data. It discusses the characteristics and appropriate uses of central tendency and dispersion measures.
The document provides an overview of statistical concepts including descriptive and inferential statistics, measures of central tendency and dispersion, hypothesis testing procedures, and examples of one-sample and two-sample hypothesis tests. Specifically, it discusses topics such as the mean, median, mode, range, variance, standard deviation, stating hypotheses, identifying test statistics, formulating decision rules, taking samples, and interpreting results. Examples are given to illustrate one-sample t-tests and two-sample z-tests for comparing population means with known and equal variances.
The document provides an overview of PSPP software and statistical analysis techniques, including:
- Descriptive statistics such as measures of central tendency (mean, median, mode), measures of dispersion (range, variance, standard deviation), and data displays (frequency tables, bar charts, pie charts, histograms)
- The difference between descriptive and inferential statistics, and an introduction to hypothesis testing including stating hypotheses, significance levels, test statistics, and decision rules.
- Examples of one-sample and two-sample hypothesis tests, comparing population means when variances are known or unknown, to determine if samples are representative of populations.
This document provides an overview of key numerical measures used to describe data, including measures of central tendency (mean, median, mode) and measures of dispersion (range, variance, standard deviation). It defines each measure, provides examples of calculating them, and discusses their characteristics, uses, and advantages/disadvantages. The document also covers weighted means, geometric means, Chebyshev's theorem, and calculating measures for grouped data.
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.
The document discusses measures of central tendency (mean, median, mode) and variation (range, interquartile range, standard deviation) used in statistics. It provides examples of calculating these values from data sets and identifying outliers. The mean is the average value, the median is the middle value, and the mode is the most frequent value. Variation measures describe how spread out the data is, with standard deviation being the most common measure of spread from the mean. Outliers are extreme values more than 3 standard deviations from the mean that can skew the mean and standard deviation.
The document provides an overview of techniques for describing and exploring data, including dot plots, stem-and-leaf displays, measures of central tendency, box plots, coefficients of skewness, scatterplots, and contingency tables. It defines each technique and provides examples to illustrate how to construct and interpret the visualizations. The learning objectives cover how to use each technique to analyze and draw conclusions from sets of quantitative data.
The document provides an overview of various techniques for describing and exploring data, including dot plots, stem-and-leaf displays, measures of position such as percentiles, box plots, skewness, scatterplots, and contingency tables. It defines each technique and provides examples of their construction and interpretation. Learning objectives cover how to construct and interpret each type of graph or statistical measure.
This document provides an overview of descriptive statistics techniques for summarizing categorical and quantitative data. It discusses frequency distributions, measures of central tendency (mean, median, mode), measures of variability (range, variance, standard deviation), and methods for visualizing data through charts, graphs, and other displays. The goal of descriptive statistics is to organize and describe the characteristics of data through counts, averages, and other summaries.
The document provides information about measures of central tendency (mean, median, mode) and measures of dispersion (range, quartiles, variance, standard deviation) using examples of data distributions. It defines key terms like mean, median, mode, range, quartiles, variance and standard deviation. It also shows how to calculate and interpret these measures of central tendency and dispersion using sample data sets.
Measures of dispersion qt pgdm 1st trisemester Karan Kukreja
This document discusses various measures of dispersion and variability used to describe the spread or scatter of data values within a data set. It defines key terms like range, quartile deviation, standard deviation, variance and coefficient of variation. It also discusses how to calculate these measures for both ungrouped and grouped data. The document explains how standard deviation measures how much the data values vary from the mean. It shows how data distributions can be visualized using a normal distribution curve in relation to standard deviation.
The document discusses measures of variability in statistics including range, interquartile range, standard deviation, and variance. It provides examples of calculating each measure using sample data sets. The range is the difference between the highest and lowest values, while the interquartile range is the difference between the third and first quartiles. The standard deviation represents the average amount of dispersion from the mean, and variance is the average of the squared deviations from the mean. Both standard deviation and variance increase with greater variability in the data set.
This document provides an overview of key concepts for describing and summarizing data, including measures of central tendency (mean, median, mode), measures of variation (range, variance, standard deviation), and concepts like skewness. It discusses how to calculate and interpret these measures for both grouped and ungrouped data sets. Examples are provided to demonstrate calculating these statistics for different types of data distributions.
This document provides a summary of key concepts from Chapter 3 of a statistics textbook, including:
- How to calculate measures of central tendency like the mean, median, mode, and weighted mean
- The characteristics and properties of each measure
- How the positions of the mean, median and mode relate to the shape of the distribution
- How to calculate the mean, median and mode for grouped data
- What the geometric mean represents and how it is calculated
The document discusses various measures of central tendency and variability used in descriptive statistics. It defines the mean as the sum of all values divided by the number of values. The median is the middle value when values are sorted in ascending order. The mode is the most frequently occurring value. Variability measures the dispersion of scores around the mean and includes the range, interquartile range, standard deviation, and variance. The interquartile range is the difference between the third and first quartiles. Covariance measures how two variables vary together and is used to calculate the correlation coefficient. Factors like extreme scores, sample size, stability under sampling, and open-ended distributions can affect measures of variability.
Measure of dispersion by Neeraj Bhandari ( Surkhet.Nepal )Neeraj Bhandari
This document discusses measures of dispersion used in statistics. It defines measures such as range, quartile deviation, mean deviation, variance, and standard deviation. It provides formulas to calculate these measures and examples showing how to apply the formulas. The key points are:
- Measures of dispersion quantify how spread out or varied the values in a data set are. They help identify variation, compare data sets, and enable other statistical techniques.
- Common absolute measures include range, quartile deviation, and mean deviation. Common relative measures include coefficient of range, coefficient of quartile deviation, and coefficient of variation.
- Variance and standard deviation are calculated using all data points. Variance is the average of squared deviations
This document provides an overview of key concepts in statistics including:
- Descriptive statistics such as frequency distributions which organize and summarize data
- Inferential statistics which make estimates or predictions about populations based on samples
- Types of variables including quantitative, qualitative, discrete and continuous
- Levels of measurement including nominal, ordinal, interval and ratio
- Common measures of central tendency (mean, median, mode) and dispersion (range, standard deviation)
This document provides an overview of descriptive statistics and statistical concepts. It discusses topics such as data collection, organization, analysis, interpretation and presentation. It also covers frequency distributions, measures of central tendency (mean, median, mode), measures of variability (range, variance, standard deviation), and hypothesis testing. Hypothesis testing involves forming a null hypothesis and alternative hypothesis, and using statistical tests to either reject or fail to reject the null hypothesis based on sample data. Common statistical tests include ones for comparing means, variances or proportions.
This document discusses descriptive statistics and exploratory data analysis. It defines descriptive statistics as procedures for summarizing quantitative data in a clear way, while exploratory data analysis involves examining data to understand its characteristics. The document outlines common descriptive statistics like the mean, median, mode, standard deviation, and frequency distributions. It also discusses examining distributions, central tendency, dispersion, and using SPSS to calculate descriptive statistics.
Frequencies, Proportion, Graphs
February 8th, 2016
Frequency, Percentages, and Proportions
Frequency number of participants or cases.
Denoted by the symbol f.
N can also mean frequency.
f=50 or N=50 had a score of 80. Both mean that 50 people had a score of 80.
Percentage, number per 100 who have a certain characteristic.
64% of registered voters are Democrats; each 100 registered voters 64 are Democrats
To determine how many are Democrats
Multiply the total number of registered voters by .64; if we have 2,200 registered voters; .64 X 2200=1408 are democrats.
2
Percentage and Proportions
Percentages
32 of 96 children reported that a dog is their favorite animal ; 32/96=.33*100=33% of these students like dogs.
Interpretation: Based on this sample, out of 100 participants from the same population, we can expect about 33 of them to report that dogs are their favorite animal.
Proportions is part of numeral 1.
Proportion of children who like dogs is .33
Meaning that 33 hundredths of the children like dogs.
Percentages are easier to interpret.
Percentages Cont’d
Good to report the sample size with the frequency
Percentages can help us understand differences between groups of individuals
College ACollege BNumber of Education MajorsN=500N=800Early Childhood EducationN= 400 (80%)N=600
(75%)
Shapes of Distributions
Frequency distribution
Number of participants have each score
Remember that we are describing our data
X (Score)f2522442352110207194181171N=34
Frequency Polygon
Histogram
Shapes of Distributions Cont’d
Normal Distribution
Most Important shape (shape found in nature)
Heights of 10 year old boys in a large population
Bell-shaped curve
Used for inferential Statistics
Skewed Distributions
Skew: most frequent scores are clustered at one end of the distribution
The symmetry of the distribution.
Positive skew (scores bunched at low values with the tail pointing to high values).
Negative skew (scores bunched at high values with the tail pointing to low values).
Consider how groups differ depending on their standard deviation.
68% of the cases lie within one standard deviation unit of the mean in a normal distribution.
95% of the cases lie within two standard deviation unit of the mean in a normal distribution
99% of the cases lie within three standard deviation unit of the mean in a normal distribution
Standard Deviation and the Normal Distribution
February 1, 2016
Descriptive Statistics
Number of Children in families
Order of finish in the Boston Marathon
Grading System (A, B, C, D, F)
Level of Blood Sugar
Time required to complete a maze
Political Party Affiliation
Amount of gasoline consumed
Majors in College
IQ scores
Number of Fatal Accidents
Level of Measurement Examples
2
Types of Statistics
We use descriptive statistics to summarize data
Think about measures of central tendency and variability
We use correlational statistics to describe the relationship between two variables
Considered as a ...
1. The document provides the scheme of work and lesson notes for Economics for Grade 11 students at Princeton College in Nigeria for the first term of the 2019/2020 school year.
2. It outlines 10 weeks of topics to be covered including basic economic tools, measures of dispersion, economic systems, and key economic indicators.
3. The lessons provide definitions, formulas, examples, and practice problems for students to learn concepts like mean, median, mode, range, variance, and standard deviation.
This document discusses various measures of dispersion used in statistics including range, quartile deviation, mean deviation, and standard deviation. It provides definitions and formulas for calculating each measure, as well as examples of calculating the measures for both ungrouped and grouped quantitative data. The key measures discussed are the range, which is the difference between the maximum and minimum values; quartile deviation, which is the difference between the third and first quartiles; mean deviation, which is the mean of the absolute deviations from the mean; and standard deviation, which is the square root of the mean of the squared deviations from the arithmetic mean.
The document discusses several key probability distributions:
- The uniform distribution is defined by minimum and maximum values and is rectangular in shape. It has a mean equal to the average of the minimum and maximum values.
- The normal distribution is bell-shaped and symmetrical about the mean. It is determined by the mean and standard deviation.
- The standard normal distribution has a mean of 0 and standard deviation of 1. It is used to convert other normal distributions.
- Various methods are described for calculating probabilities using the normal, uniform, and binomial distributions including using the empirical rule and normal approximation to the binomial. The continuity correction is discussed for approximating binomial with normal.
This document discusses several key probability distributions: binomial, hypergeometric, and Poisson. It begins by defining probability distributions and their key characteristics. It then distinguishes between discrete and continuous random variables. The document provides examples of calculating the mean, variance, and standard deviation of probability distributions. It also gives examples of computing probabilities for binomial, hypergeometric, and Poisson distributions through formulas and real world scenarios.
This document provides an overview of key numerical measures used to describe data, including measures of central tendency (mean, median, mode) and measures of dispersion (range, variance, standard deviation). It defines each measure, provides examples of calculating them, and discusses their characteristics, uses, and advantages/disadvantages. The document also covers weighted means, geometric means, Chebyshev's theorem, and calculating measures for grouped data.
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.
The document discusses measures of central tendency (mean, median, mode) and variation (range, interquartile range, standard deviation) used in statistics. It provides examples of calculating these values from data sets and identifying outliers. The mean is the average value, the median is the middle value, and the mode is the most frequent value. Variation measures describe how spread out the data is, with standard deviation being the most common measure of spread from the mean. Outliers are extreme values more than 3 standard deviations from the mean that can skew the mean and standard deviation.
The document provides an overview of techniques for describing and exploring data, including dot plots, stem-and-leaf displays, measures of central tendency, box plots, coefficients of skewness, scatterplots, and contingency tables. It defines each technique and provides examples to illustrate how to construct and interpret the visualizations. The learning objectives cover how to use each technique to analyze and draw conclusions from sets of quantitative data.
The document provides an overview of various techniques for describing and exploring data, including dot plots, stem-and-leaf displays, measures of position such as percentiles, box plots, skewness, scatterplots, and contingency tables. It defines each technique and provides examples of their construction and interpretation. Learning objectives cover how to construct and interpret each type of graph or statistical measure.
This document provides an overview of descriptive statistics techniques for summarizing categorical and quantitative data. It discusses frequency distributions, measures of central tendency (mean, median, mode), measures of variability (range, variance, standard deviation), and methods for visualizing data through charts, graphs, and other displays. The goal of descriptive statistics is to organize and describe the characteristics of data through counts, averages, and other summaries.
The document provides information about measures of central tendency (mean, median, mode) and measures of dispersion (range, quartiles, variance, standard deviation) using examples of data distributions. It defines key terms like mean, median, mode, range, quartiles, variance and standard deviation. It also shows how to calculate and interpret these measures of central tendency and dispersion using sample data sets.
Measures of dispersion qt pgdm 1st trisemester Karan Kukreja
This document discusses various measures of dispersion and variability used to describe the spread or scatter of data values within a data set. It defines key terms like range, quartile deviation, standard deviation, variance and coefficient of variation. It also discusses how to calculate these measures for both ungrouped and grouped data. The document explains how standard deviation measures how much the data values vary from the mean. It shows how data distributions can be visualized using a normal distribution curve in relation to standard deviation.
The document discusses measures of variability in statistics including range, interquartile range, standard deviation, and variance. It provides examples of calculating each measure using sample data sets. The range is the difference between the highest and lowest values, while the interquartile range is the difference between the third and first quartiles. The standard deviation represents the average amount of dispersion from the mean, and variance is the average of the squared deviations from the mean. Both standard deviation and variance increase with greater variability in the data set.
This document provides an overview of key concepts for describing and summarizing data, including measures of central tendency (mean, median, mode), measures of variation (range, variance, standard deviation), and concepts like skewness. It discusses how to calculate and interpret these measures for both grouped and ungrouped data sets. Examples are provided to demonstrate calculating these statistics for different types of data distributions.
This document provides a summary of key concepts from Chapter 3 of a statistics textbook, including:
- How to calculate measures of central tendency like the mean, median, mode, and weighted mean
- The characteristics and properties of each measure
- How the positions of the mean, median and mode relate to the shape of the distribution
- How to calculate the mean, median and mode for grouped data
- What the geometric mean represents and how it is calculated
The document discusses various measures of central tendency and variability used in descriptive statistics. It defines the mean as the sum of all values divided by the number of values. The median is the middle value when values are sorted in ascending order. The mode is the most frequently occurring value. Variability measures the dispersion of scores around the mean and includes the range, interquartile range, standard deviation, and variance. The interquartile range is the difference between the third and first quartiles. Covariance measures how two variables vary together and is used to calculate the correlation coefficient. Factors like extreme scores, sample size, stability under sampling, and open-ended distributions can affect measures of variability.
Measure of dispersion by Neeraj Bhandari ( Surkhet.Nepal )Neeraj Bhandari
This document discusses measures of dispersion used in statistics. It defines measures such as range, quartile deviation, mean deviation, variance, and standard deviation. It provides formulas to calculate these measures and examples showing how to apply the formulas. The key points are:
- Measures of dispersion quantify how spread out or varied the values in a data set are. They help identify variation, compare data sets, and enable other statistical techniques.
- Common absolute measures include range, quartile deviation, and mean deviation. Common relative measures include coefficient of range, coefficient of quartile deviation, and coefficient of variation.
- Variance and standard deviation are calculated using all data points. Variance is the average of squared deviations
This document provides an overview of key concepts in statistics including:
- Descriptive statistics such as frequency distributions which organize and summarize data
- Inferential statistics which make estimates or predictions about populations based on samples
- Types of variables including quantitative, qualitative, discrete and continuous
- Levels of measurement including nominal, ordinal, interval and ratio
- Common measures of central tendency (mean, median, mode) and dispersion (range, standard deviation)
This document provides an overview of descriptive statistics and statistical concepts. It discusses topics such as data collection, organization, analysis, interpretation and presentation. It also covers frequency distributions, measures of central tendency (mean, median, mode), measures of variability (range, variance, standard deviation), and hypothesis testing. Hypothesis testing involves forming a null hypothesis and alternative hypothesis, and using statistical tests to either reject or fail to reject the null hypothesis based on sample data. Common statistical tests include ones for comparing means, variances or proportions.
This document discusses descriptive statistics and exploratory data analysis. It defines descriptive statistics as procedures for summarizing quantitative data in a clear way, while exploratory data analysis involves examining data to understand its characteristics. The document outlines common descriptive statistics like the mean, median, mode, standard deviation, and frequency distributions. It also discusses examining distributions, central tendency, dispersion, and using SPSS to calculate descriptive statistics.
Frequencies, Proportion, Graphs
February 8th, 2016
Frequency, Percentages, and Proportions
Frequency number of participants or cases.
Denoted by the symbol f.
N can also mean frequency.
f=50 or N=50 had a score of 80. Both mean that 50 people had a score of 80.
Percentage, number per 100 who have a certain characteristic.
64% of registered voters are Democrats; each 100 registered voters 64 are Democrats
To determine how many are Democrats
Multiply the total number of registered voters by .64; if we have 2,200 registered voters; .64 X 2200=1408 are democrats.
2
Percentage and Proportions
Percentages
32 of 96 children reported that a dog is their favorite animal ; 32/96=.33*100=33% of these students like dogs.
Interpretation: Based on this sample, out of 100 participants from the same population, we can expect about 33 of them to report that dogs are their favorite animal.
Proportions is part of numeral 1.
Proportion of children who like dogs is .33
Meaning that 33 hundredths of the children like dogs.
Percentages are easier to interpret.
Percentages Cont’d
Good to report the sample size with the frequency
Percentages can help us understand differences between groups of individuals
College ACollege BNumber of Education MajorsN=500N=800Early Childhood EducationN= 400 (80%)N=600
(75%)
Shapes of Distributions
Frequency distribution
Number of participants have each score
Remember that we are describing our data
X (Score)f2522442352110207194181171N=34
Frequency Polygon
Histogram
Shapes of Distributions Cont’d
Normal Distribution
Most Important shape (shape found in nature)
Heights of 10 year old boys in a large population
Bell-shaped curve
Used for inferential Statistics
Skewed Distributions
Skew: most frequent scores are clustered at one end of the distribution
The symmetry of the distribution.
Positive skew (scores bunched at low values with the tail pointing to high values).
Negative skew (scores bunched at high values with the tail pointing to low values).
Consider how groups differ depending on their standard deviation.
68% of the cases lie within one standard deviation unit of the mean in a normal distribution.
95% of the cases lie within two standard deviation unit of the mean in a normal distribution
99% of the cases lie within three standard deviation unit of the mean in a normal distribution
Standard Deviation and the Normal Distribution
February 1, 2016
Descriptive Statistics
Number of Children in families
Order of finish in the Boston Marathon
Grading System (A, B, C, D, F)
Level of Blood Sugar
Time required to complete a maze
Political Party Affiliation
Amount of gasoline consumed
Majors in College
IQ scores
Number of Fatal Accidents
Level of Measurement Examples
2
Types of Statistics
We use descriptive statistics to summarize data
Think about measures of central tendency and variability
We use correlational statistics to describe the relationship between two variables
Considered as a ...
1. The document provides the scheme of work and lesson notes for Economics for Grade 11 students at Princeton College in Nigeria for the first term of the 2019/2020 school year.
2. It outlines 10 weeks of topics to be covered including basic economic tools, measures of dispersion, economic systems, and key economic indicators.
3. The lessons provide definitions, formulas, examples, and practice problems for students to learn concepts like mean, median, mode, range, variance, and standard deviation.
This document discusses various measures of dispersion used in statistics including range, quartile deviation, mean deviation, and standard deviation. It provides definitions and formulas for calculating each measure, as well as examples of calculating the measures for both ungrouped and grouped quantitative data. The key measures discussed are the range, which is the difference between the maximum and minimum values; quartile deviation, which is the difference between the third and first quartiles; mean deviation, which is the mean of the absolute deviations from the mean; and standard deviation, which is the square root of the mean of the squared deviations from the arithmetic mean.
The document discusses several key probability distributions:
- The uniform distribution is defined by minimum and maximum values and is rectangular in shape. It has a mean equal to the average of the minimum and maximum values.
- The normal distribution is bell-shaped and symmetrical about the mean. It is determined by the mean and standard deviation.
- The standard normal distribution has a mean of 0 and standard deviation of 1. It is used to convert other normal distributions.
- Various methods are described for calculating probabilities using the normal, uniform, and binomial distributions including using the empirical rule and normal approximation to the binomial. The continuity correction is discussed for approximating binomial with normal.
This document discusses several key probability distributions: binomial, hypergeometric, and Poisson. It begins by defining probability distributions and their key characteristics. It then distinguishes between discrete and continuous random variables. The document provides examples of calculating the mean, variance, and standard deviation of probability distributions. It also gives examples of computing probabilities for binomial, hypergeometric, and Poisson distributions through formulas and real world scenarios.
The document provides an overview of probability concepts including:
- Defining probability as a value between 0 and 1 describing the likelihood of an event.
- Explaining experiment, outcome, and event.
- Identifying the three approaches to assigning probabilities: classical, empirical, and subjective.
- Explaining rules of addition, multiplication, and conditional probability for calculating probabilities.
- Describing how to calculate probabilities using contingency tables, Bayes' theorem, and principles of counting such as permutations and combinations.
This document discusses various methods for summarizing and presenting data, including frequency tables, bar charts, pie charts, frequency distributions, histograms, and frequency polygons. It provides examples using vehicle sales profit data from Applewood Auto Group to demonstrate how to create these different data summaries and visualizations. The learning objectives cover how to make a frequency table, organize data into bar and pie charts, create a frequency distribution, understand relative frequency distributions, and present data from distributions in histograms and frequency polygons.
This document provides an overview of key statistical concepts. It discusses descriptive statistics which organize and summarize data, and inferential statistics which make generalizations from samples to populations. It defines a population as all possible values and a sample as a subset of the population. Variables are described as either qualitative involving categories or quantitative involving numbers, with quantitative variables further divided into discrete using separate values or continuous using any value in a range. Finally, it outlines the four levels of measurement for data - nominal involving simple categories, ordinal as categories with a rank order, interval where differences are meaningful, and ratio where a true zero value exists.
The document discusses market regulation and its economic effects. It analyzes the differences between economic regulation, which directly limits competition, and social regulation, which increases costs. Both reduce economic efficiency by raising prices, lowering quantity, creating deadweight loss, and limiting competition and consumer choice. Regulation often benefits special interests groups at the expense of consumers. Markets are generally more efficient than regulation at achieving social goals.
Best practices for project execution and deliveryCLIVE MINCHIN
A select set of project management best practices to keep your project on-track, on-cost and aligned to scope. Many firms have don't have the necessary skills, diligence, methods and oversight of their projects; this leads to slippage, higher costs and longer timeframes. Often firms have a history of projects that simply failed to move the needle. These best practices will help your firm avoid these pitfalls but they require fortitude to apply.
Part 2 Deep Dive: Navigating the 2024 Slowdownjeffkluth1
Introduction
The global retail industry has weathered numerous storms, with the financial crisis of 2008 serving as a poignant reminder of the sector's resilience and adaptability. However, as we navigate the complex landscape of 2024, retailers face a unique set of challenges that demand innovative strategies and a fundamental shift in mindset. This white paper contrasts the impact of the 2008 recession on the retail sector with the current headwinds retailers are grappling with, while offering a comprehensive roadmap for success in this new paradigm.
Understanding User Needs and Satisfying ThemAggregage
https://www.productmanagementtoday.com/frs/26903918/understanding-user-needs-and-satisfying-them
We know we want to create products which our customers find to be valuable. Whether we label it as customer-centric or product-led depends on how long we've been doing product management. There are three challenges we face when doing this. The obvious challenge is figuring out what our users need; the non-obvious challenges are in creating a shared understanding of those needs and in sensing if what we're doing is meeting those needs.
In this webinar, we won't focus on the research methods for discovering user-needs. We will focus on synthesis of the needs we discover, communication and alignment tools, and how we operationalize addressing those needs.
Industry expert Scott Sehlhorst will:
• Introduce a taxonomy for user goals with real world examples
• Present the Onion Diagram, a tool for contextualizing task-level goals
• Illustrate how customer journey maps capture activity-level and task-level goals
• Demonstrate the best approach to selection and prioritization of user-goals to address
• Highlight the crucial benchmarks, observable changes, in ensuring fulfillment of customer needs
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Unveiling the Dynamic Personalities, Key Dates, and Horoscope Insights: Gemin...my Pandit
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2. Learning Objectives
LO1 Explain the concept of central tendency.
LO2 Identify and compute the arithmetic mean.
LO3 Compute and interpret the weighted mean.
LO4 Determine the median.
LO5 Identify the mode.
LO6 Calculate the geometric mean.
LO7 Explain and apply measures of dispersion.
LO8 Compute and interpret the standard deviation.
LO9 Explain Chebyshev’s Theorem and the Empirical
Rule.
L10 Compute the mean and standard deviation of
grouped data.
3-2
3. Central Tendency -
Measures of Location
The purpose of a measure of location is to
pinpoint the center of a distribution of data.
There are many measures of location. We
will consider five:
1. The arithmetic mean,
2. The weighted mean,
3. The median,
4. The mode, and
5. The geometric mean
LO1 Explain the concept
of central tendency
3-3
4. Characteristics of the Mean
The arithmetic mean is the most widely used
measure of location.
Requires the interval scale.
Major characteristics:
All values are used.
It is unique.
The sum of the deviations from the mean is 0.
It is calculated by summing the values and
dividing by the number of values.
LO2 Identify and compute
the arithmetic mean.
3-4
5. Population Mean
For ungrouped data, the population mean is the
sum of all the population values divided by the
total number of population values:
LO2
3-5
6. EXAMPLE – Population Mean
LO2
There are 42 exits on I-75 through the state of Kentucky.
Listed below are the distances between exits (in miles).
Why is this information a population?
What is the mean number of miles between exits?
3-6
7. EXAMPLE – Population Mean
LO2
There are 42 exits on I-75 through the state of Kentucky. Listed below are the
distances between exits (in miles).
Why is this information a population?
This is a population because we are considering all the exits in Kentucky.
What is the mean number of miles between exits?
3-7
9. Properties of the Arithmetic Mean
1. Every set of interval-level and ratio-level data has a
mean.
2. All the values are included in computing the mean.
3. The mean is unique.
4. The sum of the deviations of each value from the mean is
zero.
LO2
3-9
10. Sample Mean
For ungrouped data, the sample mean is the
sum of all the sample values divided by the
number of sample values:
LO2
3-10
12. Weighted Mean
The weighted mean of a set of numbers X1,
X2, ..., Xn, with corresponding weights w1,
w2, ...,wn, is computed from the following
formula:
LO3 Compute and interpret
the weighted mean
3-12
13. EXAMPLE – Weighted Mean
The Carter Construction Company pays its hourly
employees $16.50, $19.00, or $25.00 per hour.
There are 26 hourly employees, 14 of which are paid
at the $16.50 rate, 10 at the $19.00 rate, and 2 at the
$25.00 rate.
What is the mean hourly rate paid the 26
employees?
LO3
3-13
14. The Median
PROPERTIES OF THE MEDIAN
1. There is a unique median for each data set.
2. It is not affected by extremely large or small values and is
therefore a valuable measure of central tendency when such
values occur.
3. It can be computed for ratio-level, interval-level, and ordinal-
level data.
4. It can be computed for an open-ended frequency distribution if
the median does not lie in an open-ended class.
MEDIAN The midpoint of the values after they have been
ordered from the smallest to the largest, or the largest to
the smallest.
LO4 Determine the median.
3-14
15. EXAMPLES - Median
The ages for a sample
of five college students
are:
21, 25, 19, 20, 22
Arranging the data in
ascending order gives:
19, 20, 21, 22, 25.
Thus the median is 21.
The heights of four
basketball players, in
inches, are:
76, 73, 80, 75
Arranging the data in
ascending order gives:
73, 75, 76, 80.
Thus the median is 75.5
LO4
3-15
16. The Mode
MODE The value of the observation that appears
most frequently.
LO5 Identify the mode.
3-16
17. Example - Mode
LO5
Using the data regarding the
distance in miles between exits
on I-75 through Kentucky. The
information is repeated below.
What is the modal distance?
Organize the distances into a
frequency table.
3-17
19. The Geometric Mean
Useful in finding the average change of percentages, ratios, indexes, or growth rates over time.
It has a wide application in business and economics because we are often interested in finding the
percentage changes in sales, salaries, or economic figures, such as the GDP, which compound or
build on each other.
The geometric mean will always be less than or equal to the arithmetic mean.
The formula for the geometric mean is written:
EXAMPLE:
The return on investment earned by Atkins Construction Company for four successive years was: 30
percent, 20 percent, -40 percent, and 200 percent. What is the geometric mean rate of return on
investment?
LO6 Calculate the geometric mean.
3-19
20. The Geometric Mean – Finding an Average
Percent Change Over Time
EXAMPLE
During the decade of the 1990s, and into the 2000s, Las Vegas, Nevada, was the fastest-growing
city in the United States. The population increased from 258,295 in 1990 to 607,876 in 2009. This is
an increase of 349,581 people, or a 135.3 percent increase over the period. The population has
more than doubled.
What is the average annual increase?
LO6
3-20
21. Dispersion
A measure of location, such as the mean or the median, only describes the center
of the data. It is valuable from that standpoint, but it does not tell us anything about
the spread of the data.
For example, if your nature guide told you that the river ahead averaged 3 feet in
depth, would you want to wade across on foot without additional information?
Probably not. You would want to know something about the variation in the depth.
A second reason for studying the dispersion in a set of data is to compare the
spread in two or more distributions.
LO7 Explain and apply
measures of dispersion.
3-21
23. EXAMPLE – Range
The number of cappuccinos sold at the Starbucks location in the
Orange Country Airport between 4 and 7 p.m. for a sample of 5
days last year were 20, 40, 50, 60, and 80. Determine the range
for the number of cappuccinos sold.
Range = Largest – Smallest value
= 80 – 20 = 60
LO7
3-23
24. Mean Deviation
A shortcoming of the range is that it is based on only two values,
the highest and the lowest; it does not take into consideration all
of the values.
The mean deviation does. It measures the mean amount by
which the values in a population, or sample, vary from their mean
MEAN DEVIATION The arithmetic mean of the absolute values
of the deviations from the arithmetic mean.
LO7
3-24
25. EXAMPLE – Mean Deviation
The number of cappuccinos sold at the Starbucks
location in the Orange Country Airport between 4
and 7 p.m. for a sample of 5 days last year were
20, 40, 50, 60, and 80.
Determine the mean deviation for the number of
cappuccinos sold.
Step 1: Compute the mean
50
5
80
60
50
40
20
n
x
x
LO7
3-25
26. EXAMPLE – Mean Deviation
Step 2: Subtract the mean (50) from each of the observations,
convert to positive if difference is negative
Step 3: Sum the absolute differences found in step 2 then divide
by the number of observations
LO7
3-26
27. Variance and Standard Deviation
The variance and standard deviations are nonnegative and are
zero only if all observations are the same.
For populations whose values are near the mean, the variance
and standard deviation will be small.
For populations whose values are dispersed from the mean, the
population variance and standard deviation will be large.
The variance overcomes the weakness of the range by using all
the values in the population
VARIANCE The arithmetic mean of the squared deviations
from the mean.
STANDARD DEVIATION The square root of the variance.
LO8 Compute and interpret
the standard deviation.
3-27
28. Variance – Formula and Computation
Steps in Computing the Variance.
Step 1: Find the mean.
Step 2: Find the difference between each observation and the mean, and
square that difference.
Step 3: Sum all the squared differences found in step 2
Step 4: Divide the sum of the squared differences by the number of items in
the population.
LO8
3-28
29. EXAMPLE – Variance and Standard Deviation
The number of traffic citations issued during the last five months in
Beaufort County, South Carolina, is reported below:
What is the population variance?
Step 1: Find the mean.
Step 2: Find the difference between each observation and the
mean, and square that difference.
Step 3: Sum all the squared differences found in step 3
Step 4: Divide the sum of the squared differences by the number
of items in the population.
29
12
348
12
10
34
...
17
19
N
x
LO8
3-29
30. EXAMPLE – Variance and Standard Deviation
The number of traffic citations issued during the last twelve months in
Beaufort County, South Carolina, is reported below:
What is the population variance?
Step 2: Find the difference between each
observation and the mean,
and square that difference.
Step 3: Sum all the squared differences found in step 3
Step 4: Divide the sum of the squared differences
by the number of items in the population.
124
12
488
,
1
)
( 2
2
N
X
LO8
3-30
32. EXAMPLE – Sample Variance
The hourly wages
for a sample of
part-time
employees at
Home Depot are:
$12, $20, $16, $18,
and $19.
What is the sample
variance?
LO8
3-32
34. Chebyshev’s Theorem
The arithmetic mean biweekly amount contributed by the
Dupree Paint employees to the company’s profit-sharing plan is
$51.54, and the standard deviation is $7.51. At least what
percent of the contributions lie within plus 3.5 standard
deviations and minus 3.5 standard deviations of the mean?
LO9 Explain Chebyshev’s
Theorem and the Empirical Rule.
3-34
36. The Arithmetic Mean of Grouped Data
LO10 Compute the mean and
standard deviation of grouped data.
3-36
37. The Arithmetic Mean of Grouped Data -
Example
Recall in Chapter 2, we
constructed a frequency
distribution for Applewood
Auto Group profit data for
180 vehicles sold. The
information is repeated on
the table. Determine the
arithmetic mean profit per
vehicle.
LO10
3-37
39. Standard Deviation of Grouped Data -
Example
Refer to the frequency distribution for the Applewood Auto
Group data used earlier. Compute the standard deviation of the
vehicle profits.
LO10
3-39