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The document discusses how to calculate standard deviation and variance for both ungrouped and grouped data. It provides step-by-step instructions for finding the mean, deviations from the mean, summing the squared deviations, and using these values to calculate standard deviation and variance through standard formulas. Standard deviation measures how spread out numbers are from the mean, while variance is the square of the standard deviation.

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Measures of variability

This document defines and provides examples of key statistical concepts used to describe and analyze variability in data sets, including range, variance, standard deviation, coefficient of variation, quartiles, and percentiles. It explains that range is the difference between the highest and lowest values, variance is the average squared deviation from the mean, and standard deviation describes how distant scores are from the mean on average. Examples are provided to demonstrate calculating these measures from data sets and interpreting what they indicate about the spread of scores.

VARIANCE

Topic: Variance
Student Name: Sonia Khan
Class: B.Ed. 2.5
Project Name: “Young Teachers' Professional Development (TPD)"
"Project Founder: Prof. Dr. Amjad Ali Arain
Faculty of Education, University of Sindh, Pakistan

Variance & standard deviation

This document defines variance and standard deviation and provides formulas and examples to calculate them. It states that variance is the average squared deviation from the mean and measures how far data points are from the average. Standard deviation tells how clustered data is around the mean and is the square root of the variance. It provides step-by-step instructions to find variance and standard deviation, including calculating the mean, deviations from the mean, summing the squared deviations, and taking the square root. Worked examples are shown to find the variance and standard deviation of students' test scores and people's heights in a room.

Variance and standard deviation

This document discusses variance and standard deviation. It defines variance as the average squared deviation from the mean of a data set. Standard deviation measures how spread out numbers are from the mean and is calculated by taking the square root of the variance. The document provides step-by-step instructions for calculating both variance and standard deviation, including examples using test score data.

Measures of central tendency

Here are the modes for the three examples:
1. The mode is 3. This value occurs most frequently among the number of errors committed by the typists.
2. The mode is 82. This value occurs most frequently among the number of fruits yielded by the mango trees.
3. The mode is 12 and 15. These values occur most frequently among the students' quiz scores.

Normal Distribution

The Normal Distribution is a symmetrical probability distribution where most results are located in the middle and few are spread on both sides. It has the shape of a bell and can entirely be described by its mean and standard deviation.

Measures of Variation

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.

Measures of variability

This document discusses different measures of variability in data sets. It outlines that variability measures the spread of a data set and identifies the most common measures as range, variance, and standard deviation. Variance is calculated as the mean of the squared deviations from the mean. Standard deviation takes the square root of the variance and provides a measure of how far data points typically are from the average.

Measures of variability

This document defines and provides examples of key statistical concepts used to describe and analyze variability in data sets, including range, variance, standard deviation, coefficient of variation, quartiles, and percentiles. It explains that range is the difference between the highest and lowest values, variance is the average squared deviation from the mean, and standard deviation describes how distant scores are from the mean on average. Examples are provided to demonstrate calculating these measures from data sets and interpreting what they indicate about the spread of scores.

VARIANCE

Topic: Variance
Student Name: Sonia Khan
Class: B.Ed. 2.5
Project Name: “Young Teachers' Professional Development (TPD)"
"Project Founder: Prof. Dr. Amjad Ali Arain
Faculty of Education, University of Sindh, Pakistan

Variance & standard deviation

This document defines variance and standard deviation and provides formulas and examples to calculate them. It states that variance is the average squared deviation from the mean and measures how far data points are from the average. Standard deviation tells how clustered data is around the mean and is the square root of the variance. It provides step-by-step instructions to find variance and standard deviation, including calculating the mean, deviations from the mean, summing the squared deviations, and taking the square root. Worked examples are shown to find the variance and standard deviation of students' test scores and people's heights in a room.

Variance and standard deviation

This document discusses variance and standard deviation. It defines variance as the average squared deviation from the mean of a data set. Standard deviation measures how spread out numbers are from the mean and is calculated by taking the square root of the variance. The document provides step-by-step instructions for calculating both variance and standard deviation, including examples using test score data.

Measures of central tendency

Here are the modes for the three examples:
1. The mode is 3. This value occurs most frequently among the number of errors committed by the typists.
2. The mode is 82. This value occurs most frequently among the number of fruits yielded by the mango trees.
3. The mode is 12 and 15. These values occur most frequently among the students' quiz scores.

Normal Distribution

The Normal Distribution is a symmetrical probability distribution where most results are located in the middle and few are spread on both sides. It has the shape of a bell and can entirely be described by its mean and standard deviation.

Measures of Variation

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.

Measures of variability

This document discusses different measures of variability in data sets. It outlines that variability measures the spread of a data set and identifies the most common measures as range, variance, and standard deviation. Variance is calculated as the mean of the squared deviations from the mean. Standard deviation takes the square root of the variance and provides a measure of how far data points typically are from the average.

4. parameter and statistic

Distinguish between Parameter and Statistic.
Calculate sample variance and sample standard deviation.
Visit the website for more services: https://cristinamontenegro92.wixsite.com/onevs

Normal distribution

The normal distribution is a continuous probability distribution that is symmetric and bell-shaped. It is defined by its mean and standard deviation. Many real-world variables are approximately normally distributed. The standard normal distribution refers to a normal distribution with a mean of 0 and standard deviation of 1. The normal distribution is commonly used to model variables and calculate probabilities related to areas under the normal curve.

Statistics "Descriptive & Inferential"

It is the science of dealing with numbers.
It is used for collection, summarization, presentation and analysis of data.

Mean Deviation

This document defines and provides the formula for calculating mean deviation, which is a measure of variation that uses all the scores in a distribution. It is more reliable than range. Mean deviation is calculated by finding the absolute difference between each score and the mean, summing the absolute differences, and dividing by the number of observations. Two examples of calculating mean deviation for sets of data are provided, along with exercises asking students to find the mean deviation of additional data sets and define standard deviation.

MEAN DEVIATION

The mean deviation is a measure of how spread out values are from the average. It is calculated by:
1) Finding the mean of all values.
2) Calculating the distance between each value and the mean.
3) Taking the average of those distances. This provides the mean deviation, which tells us how far on average values are from the central mean. Examples show calculating mean deviation for both grouped and ungrouped data sets.

Mean for Grouped Data

This document discusses measures of central tendency, specifically how to calculate the mean of grouped data. It provides the formula for calculating the mean of grouped data and walks through an example of finding the mean test scores of students. The document demonstrates how to find the midpoint of each score group, multiply by the frequency, sum the results, and divide by the total frequency to determine the mean.

Mean, Median, Mode: Measures of Central Tendency

There are three common measures of central tendency: mean, median, and mode. The mean is the average value found by dividing the sum of all values by the total number of values. The median is the middle value when values are arranged from lowest to highest. The mode is the value that occurs most frequently. Each measure provides a single number to represent the central or typical value in a data set.

Measures of dispersion

This document provides an overview of measures of dispersion, including range, quartile deviation, mean deviation, standard deviation, and variance. It defines dispersion as a measure of how scattered data values are around a central value like the mean. Different measures of dispersion are described and formulas are provided. The standard deviation is identified as the most useful measure as it considers all data values and is not overly influenced by outliers. Examples are included to demonstrate calculating measures of dispersion.

Statistics-Measures of dispersions

This document discusses various measures of dispersion in statistics including range, mean deviation, variance, and standard deviation. It provides definitions and formulas for calculating each measure along with examples using both ungrouped and grouped frequency distribution data. Box-and-whisker plots are also introduced as a graphical method to display the five number summary of a data set including minimum, quartiles, and maximum values.

T distribution

The t distribution is used when sample sizes are small to determine the probability of obtaining a given sample mean. It is similar to the normal distribution but has fatter tails. Properties include having a mean of 0 and a variance that decreases and approaches 1 as the degrees of freedom increase. The t distribution approaches the normal distribution as the sample size increases to infinity or the degrees of freedom become very large. Examples show how to find t-scores, critical values, and confidence intervals using a t-table based on the sample size and desired confidence level.

6. point and interval estimation

1. Illustrate point and interval estimations.
2. Distinguish between point and interval estimation.
Visit the website for more services it can offer:
https://cristinamontenegro92.wixsite.com/onevs

quartiles,deciles,percentiles.ppt

This document defines and discusses quartiles, deciles, and percentiles. Quartiles divide a data set into four equal parts, with the first quartile (Q1) representing the lowest 25% of values. Deciles divide data into ten equal parts. Percentiles indicate the value below which a certain percentage of observations fall. Examples are provided for calculating Q1, Q3, D1 using formulas for grouped and ungrouped data sets. Quartiles, deciles, and percentiles are commonly used to summarize and report on statistical data.

The sampling distribution

The document defines a sampling distribution of sample means as a distribution of means from random samples of a population. The mean of sample means equals the population mean, and the standard deviation of sample means is smaller than the population standard deviation, equaling it divided by the square root of the sample size. As sample size increases, the distribution of sample means approaches a normal distribution according to the Central Limit Theorem.

Measures of dispersion

Measures of dispersion
Absolute measure, relative measures
Range of Coe. of Range
Mean deviation and coe. of mean deviation
Quartile deviation IQR, coefficient of QD
Standard deviation and coefficient of variation

Sampling and sampling distributions

1. The document discusses different sampling methods including simple random sampling, systematic random sampling, stratified sampling, and cluster sampling.
2. It provides examples of how each sampling method works and how samples are selected from the overall population.
3. Exercises are provided to determine which sampling method should be used for different scenarios involving selecting samples from identified populations.

Introduction to Statistics and Probability

This document provides an introduction to statistics and probability. It discusses key concepts in descriptive statistics including measures of central tendency (mean, median, mode), measures of dispersion (range, standard deviation), and measures of shape (skewness, kurtosis). It also covers correlation analysis, regression analysis, and foundational probability topics such as sample spaces, events, independent and dependent events, and theorems like the addition rule, multiplication rule, and total probability theorem.

Normal curve

The document discusses the normal curve and its key properties. A normal curve is a bell-shaped distribution that is symmetrical around the mean value, with half of the data falling above and half below the mean. The standard deviation measures how spread out the data is from the mean. In a normal distribution, 68% of the data lies within 1 standard deviation of the mean, 95% within 2 standard deviations, and 99.7% within 3 standard deviations, following the 68-95-99.7 rule.

frequency distribution

This document discusses frequency distributions and how to construct them from raw data. It provides examples of creating stem-and-leaf displays, frequency tables, relative frequency tables, and cumulative frequency tables from various data sets. Key concepts covered include class width, class boundaries, tallying data, and calculating relative frequencies and percentages. Overall, the document serves as a tutorial on how to organize and summarize data using various types of frequency distributions.

Measures of Variability

This document discusses measures of variability, which refer to how spread out a set of data is. Variability is measured using the standard deviation and variance. The standard deviation measures how far data points are from the mean, while the variance is the average of the squared deviations from the mean. To calculate the standard deviation, you take the square root of the variance. This provides a measure of variability that is on the same scale as the original data. The standard deviation and variance are widely used statistical measures for quantifying the spread of a data set.

Mode

The mode is defined as the score that occurs most frequently in a data set. It is a measure of central tendency that indicates the most common value. For an ungrouped data set, the mode is simply the value that repeats most. For a grouped data set, the mode is calculated using a formula that finds the midpoint of the interval with the highest frequency while accounting for the differences in frequencies on either side of that interval. The mode is useful when wanting a quick approximation of central tendency or when trying to find the most typical value in a data set. Data sets can have one, two, or more modes depending on the number of most frequent values.

Standard deviation

The document discusses the conceptual definition of standard deviation. Standard deviation represents the root average of the squared deviations of scores from the mean. It explains that to calculate standard deviation, each score's deviation from the mean is squared, those squared deviations are averaged, and then the square root of the average is taken to determine the standard deviation in the original units of measurement.

Standard deviation (3)

The document discusses how to calculate variance and standard deviation. It provides the formulas and steps to find variance as the average squared deviation from the mean. Standard deviation is defined as the square root of variance and measures how dispersed data are from the mean, with a larger standard deviation indicating more variation. Examples are worked through to demonstrate calculating variance and standard deviation for different data sets.

4. parameter and statistic

Distinguish between Parameter and Statistic.
Calculate sample variance and sample standard deviation.
Visit the website for more services: https://cristinamontenegro92.wixsite.com/onevs

Normal distribution

The normal distribution is a continuous probability distribution that is symmetric and bell-shaped. It is defined by its mean and standard deviation. Many real-world variables are approximately normally distributed. The standard normal distribution refers to a normal distribution with a mean of 0 and standard deviation of 1. The normal distribution is commonly used to model variables and calculate probabilities related to areas under the normal curve.

Statistics "Descriptive & Inferential"

It is the science of dealing with numbers.
It is used for collection, summarization, presentation and analysis of data.

Mean Deviation

This document defines and provides the formula for calculating mean deviation, which is a measure of variation that uses all the scores in a distribution. It is more reliable than range. Mean deviation is calculated by finding the absolute difference between each score and the mean, summing the absolute differences, and dividing by the number of observations. Two examples of calculating mean deviation for sets of data are provided, along with exercises asking students to find the mean deviation of additional data sets and define standard deviation.

MEAN DEVIATION

The mean deviation is a measure of how spread out values are from the average. It is calculated by:
1) Finding the mean of all values.
2) Calculating the distance between each value and the mean.
3) Taking the average of those distances. This provides the mean deviation, which tells us how far on average values are from the central mean. Examples show calculating mean deviation for both grouped and ungrouped data sets.

Mean for Grouped Data

This document discusses measures of central tendency, specifically how to calculate the mean of grouped data. It provides the formula for calculating the mean of grouped data and walks through an example of finding the mean test scores of students. The document demonstrates how to find the midpoint of each score group, multiply by the frequency, sum the results, and divide by the total frequency to determine the mean.

Mean, Median, Mode: Measures of Central Tendency

There are three common measures of central tendency: mean, median, and mode. The mean is the average value found by dividing the sum of all values by the total number of values. The median is the middle value when values are arranged from lowest to highest. The mode is the value that occurs most frequently. Each measure provides a single number to represent the central or typical value in a data set.

Measures of dispersion

This document provides an overview of measures of dispersion, including range, quartile deviation, mean deviation, standard deviation, and variance. It defines dispersion as a measure of how scattered data values are around a central value like the mean. Different measures of dispersion are described and formulas are provided. The standard deviation is identified as the most useful measure as it considers all data values and is not overly influenced by outliers. Examples are included to demonstrate calculating measures of dispersion.

Statistics-Measures of dispersions

This document discusses various measures of dispersion in statistics including range, mean deviation, variance, and standard deviation. It provides definitions and formulas for calculating each measure along with examples using both ungrouped and grouped frequency distribution data. Box-and-whisker plots are also introduced as a graphical method to display the five number summary of a data set including minimum, quartiles, and maximum values.

T distribution

The t distribution is used when sample sizes are small to determine the probability of obtaining a given sample mean. It is similar to the normal distribution but has fatter tails. Properties include having a mean of 0 and a variance that decreases and approaches 1 as the degrees of freedom increase. The t distribution approaches the normal distribution as the sample size increases to infinity or the degrees of freedom become very large. Examples show how to find t-scores, critical values, and confidence intervals using a t-table based on the sample size and desired confidence level.

6. point and interval estimation

1. Illustrate point and interval estimations.
2. Distinguish between point and interval estimation.
Visit the website for more services it can offer:
https://cristinamontenegro92.wixsite.com/onevs

quartiles,deciles,percentiles.ppt

This document defines and discusses quartiles, deciles, and percentiles. Quartiles divide a data set into four equal parts, with the first quartile (Q1) representing the lowest 25% of values. Deciles divide data into ten equal parts. Percentiles indicate the value below which a certain percentage of observations fall. Examples are provided for calculating Q1, Q3, D1 using formulas for grouped and ungrouped data sets. Quartiles, deciles, and percentiles are commonly used to summarize and report on statistical data.

The sampling distribution

The document defines a sampling distribution of sample means as a distribution of means from random samples of a population. The mean of sample means equals the population mean, and the standard deviation of sample means is smaller than the population standard deviation, equaling it divided by the square root of the sample size. As sample size increases, the distribution of sample means approaches a normal distribution according to the Central Limit Theorem.

Measures of dispersion

Measures of dispersion
Absolute measure, relative measures
Range of Coe. of Range
Mean deviation and coe. of mean deviation
Quartile deviation IQR, coefficient of QD
Standard deviation and coefficient of variation

Sampling and sampling distributions

1. The document discusses different sampling methods including simple random sampling, systematic random sampling, stratified sampling, and cluster sampling.
2. It provides examples of how each sampling method works and how samples are selected from the overall population.
3. Exercises are provided to determine which sampling method should be used for different scenarios involving selecting samples from identified populations.

Introduction to Statistics and Probability

This document provides an introduction to statistics and probability. It discusses key concepts in descriptive statistics including measures of central tendency (mean, median, mode), measures of dispersion (range, standard deviation), and measures of shape (skewness, kurtosis). It also covers correlation analysis, regression analysis, and foundational probability topics such as sample spaces, events, independent and dependent events, and theorems like the addition rule, multiplication rule, and total probability theorem.

Normal curve

The document discusses the normal curve and its key properties. A normal curve is a bell-shaped distribution that is symmetrical around the mean value, with half of the data falling above and half below the mean. The standard deviation measures how spread out the data is from the mean. In a normal distribution, 68% of the data lies within 1 standard deviation of the mean, 95% within 2 standard deviations, and 99.7% within 3 standard deviations, following the 68-95-99.7 rule.

frequency distribution

This document discusses frequency distributions and how to construct them from raw data. It provides examples of creating stem-and-leaf displays, frequency tables, relative frequency tables, and cumulative frequency tables from various data sets. Key concepts covered include class width, class boundaries, tallying data, and calculating relative frequencies and percentages. Overall, the document serves as a tutorial on how to organize and summarize data using various types of frequency distributions.

Measures of Variability

This document discusses measures of variability, which refer to how spread out a set of data is. Variability is measured using the standard deviation and variance. The standard deviation measures how far data points are from the mean, while the variance is the average of the squared deviations from the mean. To calculate the standard deviation, you take the square root of the variance. This provides a measure of variability that is on the same scale as the original data. The standard deviation and variance are widely used statistical measures for quantifying the spread of a data set.

Mode

The mode is defined as the score that occurs most frequently in a data set. It is a measure of central tendency that indicates the most common value. For an ungrouped data set, the mode is simply the value that repeats most. For a grouped data set, the mode is calculated using a formula that finds the midpoint of the interval with the highest frequency while accounting for the differences in frequencies on either side of that interval. The mode is useful when wanting a quick approximation of central tendency or when trying to find the most typical value in a data set. Data sets can have one, two, or more modes depending on the number of most frequent values.

4. parameter and statistic

4. parameter and statistic

Normal distribution

Normal distribution

Statistics "Descriptive & Inferential"

Statistics "Descriptive & Inferential"

Mean Deviation

Mean Deviation

MEAN DEVIATION

MEAN DEVIATION

Mean for Grouped Data

Mean for Grouped Data

Mean, Median, Mode: Measures of Central Tendency

Mean, Median, Mode: Measures of Central Tendency

Measures of dispersion

Measures of dispersion

Statistics-Measures of dispersions

Statistics-Measures of dispersions

T distribution

T distribution

6. point and interval estimation

6. point and interval estimation

quartiles,deciles,percentiles.ppt

quartiles,deciles,percentiles.ppt

The sampling distribution

The sampling distribution

Measures of dispersion

Measures of dispersion

Sampling and sampling distributions

Sampling and sampling distributions

Introduction to Statistics and Probability

Introduction to Statistics and Probability

Normal curve

Normal curve

frequency distribution

frequency distribution

Measures of Variability

Measures of Variability

Mode

Mode

Standard deviation

The document discusses the conceptual definition of standard deviation. Standard deviation represents the root average of the squared deviations of scores from the mean. It explains that to calculate standard deviation, each score's deviation from the mean is squared, those squared deviations are averaged, and then the square root of the average is taken to determine the standard deviation in the original units of measurement.

Standard deviation (3)

The document discusses how to calculate variance and standard deviation. It provides the formulas and steps to find variance as the average squared deviation from the mean. Standard deviation is defined as the square root of variance and measures how dispersed data are from the mean, with a larger standard deviation indicating more variation. Examples are worked through to demonstrate calculating variance and standard deviation for different data sets.

Descriptive statistics

This document discusses descriptive statistics and how they are used to summarize and describe data. Descriptive statistics allow researchers to analyze patterns in data but cannot be used to draw conclusions beyond the sample. Key aspects covered include measures of central tendency like mean, median, and mode to describe the central position in a data set. Measures of dispersion like range and standard deviation are also discussed to quantify how spread out the data values are. Frequency distributions are described as a way to summarize the frequencies of individual data values or ranges.

Teaching Demo

The document outlines a lesson plan for a teaching demo aimed at improving 13 to 15 year old students' writing skills based on their interests and daily lives. The lesson uses posters of different sports and activities to spark discussion and brainstorming about popular sports. Students are then given a worksheet to write sentences using different sports verbs like "do", "play", and "go". The lesson concludes with a thank you from the instructors.

Standard Deviation

Standard deviation is a measure of how spread out numbers are in a data set from the mean. It is calculated by taking the difference of each value from the mean, squaring the differences, summing them, and dividing by the number of values minus one, then taking the square root. The higher the standard deviation, the more varied the data.

Calculation of arithmetic mean

The document discusses different methods to calculate arithmetic mean from various types of data series.
It explains the direct and shortcut methods to find the arithmetic mean for individual, discrete and continuous data series.
For individual series, the direct method sums all data points and divides by the total number of data points. The shortcut method assumes a mean, calculates the differences from the assumed mean, and finds the mean as the assumed mean plus the sum of the differences divided by the total number of data points.

2.3 Histogram/Frequency Polygon/Ogives

This document discusses different types of graphs used to represent frequency distributions: histograms, frequency polygons, and ogives. It provides examples and instructions for constructing each graph type. Histograms use vertical bars to represent frequencies, frequency polygons connect points plotted for class midpoints, and ogives show cumulative frequencies. The document also discusses relative frequency graphs and common distribution shapes like bell-shaped, uniform, and skewed. It assigns practice constructing different graph types from example data.

ARITHMETIC MEAN AND SERIES

Arithmetic Mean and Series
Prepared by:
Darwin Joseph Santos
Mark Joseph Salazar
Cluadine Doma
Maricon Hollon
Randolph Sampang

First order non-linear partial differential equation & its applications

There are five types of methods for solving first order non-linear partial differential equations:
I) Equations containing only p and q variables. II) Equations relating z as a function of u. III) Equations that can be separated into functions of single variables. IV) Clairaut's Form where the solution is directly substituted. V) Charpit's Method which is a general method taking integrals of auxiliary equations to solve dz=pdx+qdy and find the solution. These types cover a range of applications including Poisson's, Helmholtz's, and Schrödinger's equations in fields like electrostatics, elasticity, wave theory and quantum mechanics.

Skewness

Skewness is a measure of the asymmetry of a distribution. A perfectly symmetrical distribution has the mean, median and mode equal, while an asymmetrical distribution has these values depart from each other. The greater the skewness, the greater the distance between the mean and mode, with the mean moving furthest from the mode due to its sensitivity to outliers. Positive skewness occurs when the mean is greater than the mode, indicating a distribution skewed to the right, while negative skewness occurs when the mean is less than the mode, indicating a left skew.

Partial Differential Equations, 3 simple examples

3 examples of PDE, for Laplace, Diffusion of Heat and Wave function. A brief definition of Fouriers Series. Slides created and compiled using LaTeX, beamer package.

Malimu variance and standard deviation

This document discusses variance and standard deviation. It defines variance as a measure of how data points differ from the mean. It explains that variance can show how two data sets that have the same mean and median can still be different. The document then provides formulas and examples for calculating variance and standard deviation. It states that standard deviation is a measure of variation from the mean and that a higher standard deviation indicates more spread and less consistency in the data.

Spearman Rank

This document explains how to use Spearman's rank correlation coefficient to determine the strength and significance of the relationship between two variables. It provides steps to calculate the coefficient using birth rate and economic development data from 12 Central and South American countries. These steps are then applied to determine if there is a correlation between life expectancy and economic development in the same countries.

Propteties of Standard Deviation

Standard deviation is a measure of how dispersed data points are from the average value. It is calculated by taking the square root of the variance, which is the average of the squared distances from the mean. For a set of egg weights, the standard deviation is calculated by first finding the mean, then determining the variance by taking the sum of the squared differences from the mean. A low standard deviation means values are close to the mean, while a high standard deviation means values are more spread out. Standard deviation is not affected by adding or subtracting a constant from all values, but is affected by multiplying or dividing all values by a constant.

Spearman Rank Correlation Presentation

The document discusses Spearman's rank correlation coefficient, a nonparametric measure of statistical dependence between two variables. It assumes values between -1 and 1, with -1 indicating a perfect negative correlation and 1 a perfect positive correlation. The steps involve converting values to ranks, calculating the differences between ranks, and determining if there is a statistically significant correlation based on the test statistic and critical values. An example calculates Spearman's rho using rankings of cricket teams in test and one day international matches.

Correlation analysis ppt

Correlation analysis measures the relationship between two or more variables. The sample correlation coefficient r ranges from -1 to 1, indicating the degree of linear relationship between variables. A value of 0 indicates no linear relationship, while values closer to 1 or -1 indicate a strong positive or negative linear relationship. Excel can be used to calculate r using the CORREL function.

Multivariate Analysis An Overview

This document provides an overview of multivariate analysis techniques, including dependency techniques like multiple regression, discriminant analysis, and MANOVA, as well as interdependency techniques like factor analysis, cluster analysis, and multidimensional scaling. It describes the uses and processes for each technique, such as using multiple regression to predict values, discriminate analysis to classify groups, and factor analysis to reduce variables. The document is signed off with warm wishes from the owner of Power Group.

Partial differential equations

The document discusses partial differential equations (PDEs). It defines PDEs and gives their general form involving independent variables, dependent variables, and partial derivatives. It describes methods for obtaining the complete integral, particular solution, singular solution, and general solution of a PDE. It provides examples of types of PDEs and how to solve them by assuming certain forms for the dependent and independent variables and their partial derivatives.

Skewness

The document contains calculations to determine skewness using grouped data. It includes frequency distributions of grouped data with ranges of values for X, frequencies (f), deviations (d), d-squared (d2), and d-cubed (d3). Formulas are provided to calculate the second (m2) and third (m3) moments about the mean. The computations are presented in a table with columns for X, M, f, fM, d, d2, d3, fd2, and fd3.

MATH Lesson Plan sample for demo teaching

This is my first made lesson plan ...
i thought before that its hard to make lesson plan but being just resourceful and with the help of different methods and strategies in teaching we can have our guide for highly and better teaching instruction:)..

Standard deviation

Standard deviation

Standard deviation (3)

Standard deviation (3)

Descriptive statistics

Descriptive statistics

Teaching Demo

Teaching Demo

Standard Deviation

Standard Deviation

Calculation of arithmetic mean

Calculation of arithmetic mean

2.3 Histogram/Frequency Polygon/Ogives

2.3 Histogram/Frequency Polygon/Ogives

ARITHMETIC MEAN AND SERIES

ARITHMETIC MEAN AND SERIES

First order non-linear partial differential equation & its applications

First order non-linear partial differential equation & its applications

Skewness

Skewness

Partial Differential Equations, 3 simple examples

Partial Differential Equations, 3 simple examples

Malimu variance and standard deviation

Malimu variance and standard deviation

Spearman Rank

Spearman Rank

Propteties of Standard Deviation

Propteties of Standard Deviation

Spearman Rank Correlation Presentation

Spearman Rank Correlation Presentation

Correlation analysis ppt

Correlation analysis ppt

Multivariate Analysis An Overview

Multivariate Analysis An Overview

Partial differential equations

Partial differential equations

Skewness

Skewness

MATH Lesson Plan sample for demo teaching

MATH Lesson Plan sample for demo teaching

Standard deviation quartile deviation

This document discusses measures of dispersion, specifically standard deviation and quartile deviation. It defines standard deviation as a measure of how closely values are clustered around the mean. Standard deviation is calculated by taking the square root of the average of the squared deviations from the mean. Quartile deviation is defined as half the difference between the third quartile (Q3) and first quartile (Q1), which divide a data set into four equal parts. The document provides examples of calculating standard deviation and quartile deviation for both individual and grouped data sets. It also discusses the merits, demerits, and uses of these statistical measures.

Measures of Spread

The document discusses various statistical concepts including range, mean deviation, variance, and standard deviation. It provides formulas and steps to calculate each measure. The range is the distance between the highest and lowest values. Mean deviation measures the average deviation from the mean. Variance is the average of the squared deviations from the mean and standard deviation is the square root of the variance, representing the average distance from the mean. Examples are given to demonstrate calculating each measure for both ungrouped and grouped data.

Sd

This document discusses standard deviation and variance as measures of how data points differ from the mean. It provides formulas for calculating population variance, sample variance, population standard deviation, and sample standard deviation. Examples are shown to demonstrate calculating variance and standard deviation from raw data. The standard deviation measures the average distance of data points from the mean and can indicate how consistently data is clustered around the mean. A lower standard deviation means data is more consistent.

Standard deviation

The document provides objectives and instructions for calculating standard deviation, variance, and student's t-test. It defines standard deviation as the positive square root of the arithmetic mean of the squared deviations from the mean. Standard deviation is considered the most reliable measure of variability. Variance is defined as the square of the standard deviation. Student's t-test is used to compare means of two samples and determine if they are statistically different. The document provides examples of calculating standard deviation, variance, and performing matched pairs and independent samples t-tests on sets of data.

Sd

1) The document discusses standard deviation and variance as measures of how dispersed data points are from the mean. It provides formulas to calculate population variance, sample variance, population standard deviation, and sample standard deviation.
2) Examples are given to demonstrate calculating variance and standard deviation from raw data sets and frequency distributions. This helps determine which data set or person is more consistent.
3) The empirical rule is described, stating that approximately 68%, 95%, and 99.7% of values in a bell-shaped distribution fall within 1, 2, and 3 standard deviations of the mean, respectively.

Variability

The document discusses variability and measures of variability. It defines variability as a quantitative measure of how spread out or clustered scores are in a distribution. The standard deviation is introduced as the most commonly used measure of variability, as it takes into account all scores in the distribution and provides the average distance of scores from the mean. Properties of the standard deviation are examined, such as how it does not change when a constant is added to all scores but does change when all scores are multiplied by a constant.

05 ch ken black solution

This document provides an outline and learning objectives for Chapter 5 of a statistics textbook on discrete distributions. The chapter will:
1. Distinguish between discrete and continuous random variables and distributions.
2. Explain how to calculate the mean and variance of discrete distributions.
3. Cover the binomial distribution and how to solve problems using it.
4. Cover the Poisson distribution and how to solve problems using it.
5. Explain how to approximate binomial problems with the Poisson distribution.
6. Cover the hypergeometric distribution and how to solve problems using it.

Overview of variance and Standard deviation.pptx

This document provides an overview of variance and standard deviation. It defines variance as the average squared deviation from the mean of a data set, and is used to calculate standard deviation. Standard deviation measures how dispersed the data is from the mean - the higher the standard deviation, the more spread out the data. It gives the formulas for calculating variance using summation notation, and standard deviation as the square root of variance. An example is shown finding the variance and standard deviation of 5 test scores.

Mean, median, and mode ug

This document defines and explains key statistical concepts including measures of central tendency (mean, median, mode), measures of dispersion (range, standard deviation), and properties of distributions (skewness, symmetry). It provides examples of calculating the mean, median, mode, and standard deviation. It also describes the empirical rule and how a certain percentage of values in a normal distribution fall within 1, 2, or 3 standard deviations of the mean.

Research Methodology anova

ANOVA (analysis of variance) is a statistical technique used to compare differences between group means. It involves calculating the F ratio, which is the ratio of variance between groups to variance within groups. If the calculated F value is greater than the critical F value from statistical tables, then the difference between group means is considered statistically significant. The document provides steps for conducting a one-way ANOVA, including calculating sums of squares, mean squares, and the F ratio to determine if differences between three varieties of wheat are statistically significant based on per acre production data.

Variance

The document defines variance as the average of the squared differences from the mean. It provides examples of calculating variance and standard deviation for different data sets involving heights of dogs, exam scores, and word counts per page. Variance is found by taking the difference of each value from the mean, squaring it, and averaging the results. Standard deviation is the square root of the variance.

Measure of dispersion

1. The document discusses various measures of dispersion used in statistics including range, quartile deviation, mean deviation, standard deviation, coefficient of variation, and coefficient of quartile deviation.
2. It provides definitions and formulas for calculating each measure. For example, it states that range is defined as the difference between the maximum and minimum values, while standard deviation is the square root of the average of the squared deviations from the mean.
3. The document also compares absolute and relative measures of dispersion. Absolute measures use numerical variations to determine error, while relative measures express dispersion as a proportion of the mean or other measure of central tendency.

3.3 Measures of Variation

This document discusses measures of variation in data, including range, variance, and standard deviation. It provides examples of calculating these measures for both individual data points and grouped data. The key measures are:
- Range is the highest value minus the lowest value.
- Variance is the average of the squared distances from the mean.
- Standard deviation is the square root of the variance, measuring average deviation from the mean.
- Coefficient of variation allows comparison of variables with different units by expressing standard deviation as a percentage of the mean.
- Chebyshev's theorem and the empirical rule specify what proportion of data falls within a given number of standard deviations of the mean.

Measure of dispersion by Neeraj Bhandari ( Surkhet.Nepal )

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

Describing Data: Numerical Measures

Numerical Measures in Statistics.arithmetic mean, weighted mean,
median, mode, and geometric mean.Measures of Dispersion

Unit-I Measures of Dispersion- Biostatistics - Ravinandan A P.pdf

Biostatistics, Unit-I, Measures of Dispersion, Dispersion
Range
variation of mean
standard deviation
Variance
coefficient of variation
standard error of the mean

18-21 Principles of Least Squares.ppt

- The document discusses principles of least squares adjustment for survey measurements.
- It introduces random error adjustment to account for measurement errors by minimizing the sum of squared residuals.
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- It presents examples to demonstrate setting up and solving least squares adjustments through normal equation matrices in both linear and nonlinear systems.

Rm class-2 part-1

This document discusses various measures of central tendency and dispersion used to summarize collected data. It defines mean, median and mode as measures of central tendency, and how to calculate each one. It also covers variance, standard deviation and coefficient of variation as measures of dispersion. The document provides examples of calculating and interpreting these statistical concepts, and explains when to use each measure to best summarize a data set.

ch-4-measures-of-variability-11 2.ppt for nursing

This document discusses measures of variability used in statistics. It defines variability as the spread or dispersion of scores. The key measures of variability discussed are the range, variance, and standard deviation. The range is the difference between the highest and lowest scores. The variance is the average of the squared deviations from the mean and represents how far the scores deviate from the mean. The standard deviation is the square root of the variance and represents how much scores typically deviate from the mean. Larger standard deviations indicate greater variability in the scores.

measures-of-variability-11.ppt

This document discusses measures of variability used in statistics. It defines variability as the spread or dispersion of scores. The key measures of variability discussed are the range, variance, and standard deviation. The range is the difference between the highest and lowest scores. The variance is the average of the squared deviations from the mean and represents how far the scores deviate from the mean. The standard deviation is the square root of the variance and represents how much scores typically deviate from the mean. Larger standard deviations indicate greater variability in the scores.

Standard deviation quartile deviation

Standard deviation quartile deviation

Measures of Spread

Measures of Spread

Sd

Sd

Standard deviation

Standard deviation

Sd

Sd

Variability

Variability

05 ch ken black solution

05 ch ken black solution

Overview of variance and Standard deviation.pptx

Overview of variance and Standard deviation.pptx

Mean, median, and mode ug

Mean, median, and mode ug

Research Methodology anova

Research Methodology anova

Variance

Variance

Measure of dispersion

Measure of dispersion

3.3 Measures of Variation

3.3 Measures of Variation

Measure of dispersion by Neeraj Bhandari ( Surkhet.Nepal )

Measure of dispersion by Neeraj Bhandari ( Surkhet.Nepal )

Describing Data: Numerical Measures

Describing Data: Numerical Measures

Unit-I Measures of Dispersion- Biostatistics - Ravinandan A P.pdf

Unit-I Measures of Dispersion- Biostatistics - Ravinandan A P.pdf

18-21 Principles of Least Squares.ppt

18-21 Principles of Least Squares.ppt

Rm class-2 part-1

Rm class-2 part-1

ch-4-measures-of-variability-11 2.ppt for nursing

ch-4-measures-of-variability-11 2.ppt for nursing

measures-of-variability-11.ppt

measures-of-variability-11.ppt

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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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- 2. OBJECTIVES The learners are expected to: a. Calculate the Standard Deviation of a given set of data. b. Calculate the Variance of a given set of data.
- 3. STANDARD DEVIATION is a special form of average deviation from the mean. is the positive square root of the arithmetic mean of the squared deviations from the mean of the distribution.
- 4. STANDARD DEVIATION is considered as the most reliable measure of variability. is affected by the individual values or items in the distribution.
- 5. Standard Deviation for Ungrouped Data
- 6. How to Calculate the Standard Deviation for Ungrouped Data 1. Find the Mean. 2. Calculate the difference between each score and the mean. 3. Square the difference between each score and the mean.
- 7. How to Calculate the Standard Deviation for Ungrouped Data 4. Add up all the squares of the difference between each score and the mean. 5. Divide the obtained sum by n – 1. 6. Extract the positive square root of the obtained quotient.
- 8. Find the Standard Deviation 35 73 35 11 35 49 35 35 35 15 35 27 210 210 Mean= 35 Mean= 35
- 9. Find the Standard Deviation x x-ẋ (x-ẋ)2 x x-ẋ (x-ẋ)2 35 0 0 73 38 1444 35 0 0 11 -24 576 35 0 0 49 14 196 35 0 0 35 0 0 35 0 0 15 -20 400 35 0 0 27 -8 64 ∑(x-ẋ)2 0 ∑(x-ẋ)2 2680
- 10. Find the Standard Deviation
- 11. How to Calculate the Standard Deviation for Grouped Data 1. Calculate the mean. 2. Get the deviations by finding the difference of each midpoint from the mean. 3. Square the deviations and find its summation. 4. Substitute in the formula.
- 12. Find the Standard Deviation Class F Midpoint FMp _ _ _ _ Limits (2) (3) (4) X Mp - X (Mp-X)2 f( Mp-X)2 (1) 28-29 4 28.5 114.0 20.14 8.36 69.89 279.56 26-27 9 26.5 238.5 20.14 6.36 40.45 364.05 24-25 12 24.5 294.0 20.14 4.36 19.01 228.12 22-23 10 22.5 225.0 20.14 2.36 5.57 55.70 20-21 17 20.5 348.5 20.14 0.36 0.13 2.21 18-19 20 18.5 370.0 20.14 -1.64 2.69 53.80 16-17 14 16.5 231.0 20.14 -3.64 13.25 185.50 14-15 9 14.5 130.5 20.14 -5.64 31.81 286.29 12-13 5 12.5 62.5 20.14 -7.64 58.37 291.85 N= ∑fMp= ∑(Mp-X)2= 100 2,014.0 1,747.08
- 13. Find the Standard Deviation
- 14. Characteristics of the Standard Deviation 1. The standard deviation is affected by the value of every observation. 2. The process of squaring the deviations before adding avoids the algebraic fallacy of disregarding the signs.
- 15. Characteristics of the Standard Deviation 3. It has a definite mathematical meaning and is perfectly adapted to algebraic treatment. 4. It is, in general, less affected by fluctuations of sampling than the other measures of dispersion.
- 16. Characteristics of the Standard Deviation 5. The standard deviation is the unit customarily used in defining areas under the normal curve of error. It has, thus, great practical utility in sampling and statistical inference.
- 17. VARIANCE is the square of the standard deviation. In short, having obtained the value of the standard deviation, you can already determine the value of the variance.
- 18. VARIANCE It follows then that similar process will be observed in calculating both standard deviation and variance. It is only the square root symbol that makes standard deviation different from variance.
- 19. Variance for Ungrouped Data
- 20. How to Calculate the Variance for Ungrouped Data 1. Find the Mean. 2. Calculate the difference between each score and the mean. 3. Square the difference between each score and the mean.
- 21. How to Calculate the Variance for Ungrouped Data 4. Add up all the squares of the difference between each score and the mean. 5. Divide the obtained sum by n – 1.
- 22. Find the Variance 35 73 35 11 35 49 35 35 35 15 35 27 210 210 Mean= 35 Mean= 35
- 23. Find the Variance x x-ẋ (x-ẋ)2 x x-ẋ (x-ẋ)2 35 0 0 73 38 1444 35 0 0 11 -24 576 35 0 0 49 14 196 35 0 0 35 0 0 35 0 0 15 -20 400 35 0 0 27 -8 64 ∑(x-ẋ)2 0 ∑(x-ẋ)2 2680
- 25. Variance for Grouped Data
- 26. How to Calculate the Variance for Grouped Data 1. Calculate the mean. 2. Get the deviations by finding the difference of each midpoint from the mean. 3. Square the deviations and find its summation. 4. Substitute in the formula.
- 27. Find the Variance Class F Midpoint FMp _ _ _ _ Limits (2) (3) (4) X Mp - X (Mp-X)2 f( Mp-X)2 (1) 28-29 4 28.5 114.0 20.14 8.36 69.89 279.56 26-27 9 26.5 238.5 20.14 6.36 40.45 364.05 24-25 12 24.5 294.0 20.14 4.36 19.01 228.12 22-23 10 22.5 225.0 20.14 2.36 5.57 55.70 20-21 17 20.5 348.5 20.14 0.36 0.13 2.21 18-19 20 18.5 370.0 20.14 -1.64 2.69 53.80 16-17 14 16.5 231.0 20.14 -3.64 13.25 185.50 14-15 9 14.5 130.5 20.14 -5.64 31.81 286.29 12-13 5 12.5 62.5 20.14 -7.64 58.37 291.85 N= ∑fMp= ∑(Mp-X)2= 100 2,014.0 1,747.08