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1. Top results related to variance definition statistics

   • Variance: Definition, Formula, Examples, Properties & FAQs

     Variance is a measurement value used to find how the data is spread with respect to the mean or the average value of the data set. It is used to find how the distribution data is spread out with respect to the mean or the average value. The symbol used to define the variance is σ2. It is the square of the Standard Deviation. 

     The are two types of variance used in statistics,

     • Sample Variance
     • Population Variance

     The population variance is used to determine how each data point in a particular population fluctuates or is spread out, while the sample variance is used to find the average of the squared deviations from the mean.

     In this article, we will learn about Variance (Sample, Population), their formulas, properties, and others in detail.

     Table of Content

     • Variance Definition
     • Types of Variance
     • Variance Example
     • Variance Formula
     • How to Calculate Variance?
     • Variance and Standard Deviation
     • Variance and Covariance
     • Variance Properties
     • Examples...

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   • Variance: Definition, Formula, Examples, Properties & FAQs

     Variance is a measurement value used to find how the data is spread with respect to the mean or the average value of the data set. It is used to find how the distribution data is spread out with respect to the mean or the average value. The symbol used to define the variance is σ2. It is the square of the Standard Deviation. 

     The are two types of variance used in statistics,

     • Sample Variance
     • Population Variance

     The population variance is used to determine how each data point in a particular population fluctuates or is spread out, while the sample variance is used to find the average of the squared deviations from the mean.

     In this article, we will learn about Variance (Sample, Population), their formulas, properties, and others in detail.

     Variance Definition

     We measure the various values of the data and these values are used for a variety of purposes. The data can be given in two types grouped data, or ungrouped (discrete) data. If the data is given in the form of class intervals it is called grouped data whereas if...

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   • Variance and Standard Deviation: Definition, Formula & Examples

     Variance and Standard Deviation are the important measures used in Mathematics and Statics to find the meaning from a large set of data. The different formulas for Variance and Standard Deviation are highly used in mathematics to determine the trends of various values in mathematics. Variance is the measure of how the data points vary according to the mean while standard deviation is the measure of the central tendency of the distribution of the data. 

     The major difference between variance and standard deviation is in their units of measurement. Standard deviation is measured in a unit similar to the units of the mean of data, whereas the variance is measured in squared units.

     Here in this article, we will learn about variance and standard deviation including their definitions, formulas, and their differences along with suitable examples in detail.

     Table of Content

     • Variance
     • Variance Formula
     • Standard Deviation
     • Standard Deviation Formula
     • Relation between Standard Deviation and Variance
     • Differences Between Standard Deviation and Variance

     VarianceVariance is defined as, “The measure of how far the set of data is dispersed from their mean value”. Variance is represented with the symbol σ2. In other words, we can also say that the variance is the average of the squared difference from the mean....

     • As each term in the variance formula is firstly squared and then their mean is found, it is always a non-negative value, i.e. mean can be either positive or can be zero but it can never be negative.
     • Variance is always measured in squared units. For example, if we have to find the variance of the height of the student in a class, and if the height of the student is given in cm then the variance is calculated in cm2. 
     • Population Variance
     • Sample Variance
     • σ2 is the Variance of the Population, 
     • N is the Number of Observation in the Population, 
     • Xi is the ith observation in the Population, and 
     • μ is the mean of the Population.
     • Standard Deviation is the square root of the variance of the given data set. It is also called root mean square deviation. 
     • Standard Deviation is a non-negative quantity i.e. it always has positive values or zero values.
     • If all the values in a data set are similar then Standard Deviation has a value close to zero. Whereas if the values in a data set are very different from each other then standard deviation has a high positive value.
     • Population Standard Deviation
     • Sample Standard Deviation
     • σ is the Standard Deviation of the Population, 
     • N is the Number of Observation in the Population, 
     • Xi is the ith observation in the Population, and  
     • μ is the mean of the Population
     • Variance is defined as the average degree through which all the values of a given data set deviate from the mean value.
     • Standard Deviation is the degree to which the values in a data set are spread out with respect to the mean value.

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   • Variance and Standard Deviation: Definition, Formula & Examples

     Variance and Standard Deviation are the important measures used in Mathematics and Statics to find the meaning from a large set of data. The different formulas for Variance and Standard Deviation are highly used in mathematics to determine the trends of various values in mathematics. Variance is the measure of how the data points vary according to the mean while standard deviation is the measure of the central tendency of the distribution of the data. 

     The major difference between variance and standard deviation is in their units of measurement. Standard deviation is measured in a unit similar to the units of the mean of data, whereas the variance is measured in squared units.

     Here in this article, we will learn about variance and standard deviation including their definitions, formulas, and their differences along with suitable examples in detail.

     Table of Content

     • Variance
     • Variance Formula
     • Standard Deviation
     • Standard Deviation Formula
     • Relation between Standard Deviation and Variance
     • Differences Between Standard Deviation and Variance

     VarianceVariance is defined as, “The measure of how far the set of data is dispersed from their mean value”. Variance is represented with the symbol σ2. In other words, we can also say that the variance is the average of the squared difference from the mean....

     • As each term in the variance formula is firstly squared and then their mean is found, it is always a non-negative value, i.e. mean can be either positive or can be zero but it can never be negative.
     • Variance is always measured in squared units. For example, if we have to find the variance of the height of the student in a class, and if the height of the student is given in cm then the variance is calculated in cm2. 
     • Population Variance
     • Sample Variance
     • σ2 is the Variance of the Population, 
     • N is the Number of Observation in the Population, 
     • Xi is the ith observation in the Population, and 
     • μ is the mean of the Population.
     • Standard Deviation is the square root of the variance of the given data set. It is also called root mean square deviation. 
     • Standard Deviation is a non-negative quantity i.e. it always has positive values or zero values.
     • If all the values in a data set are similar then Standard Deviation has a value close to zero. Whereas if the values in a data set are very different from each other then standard deviation has a high positive value.
     • Population Standard Deviation
     • Sample Standard Deviation
     • σ is the Standard Deviation of the Population, 
     • N is the Number of Observation in the Population, 
     • Xi is the ith observation in the Population, and  
     • μ is the mean of the Population
     • Variance is defined as the average degree through which all the values of a given data set deviate from the mean value.
     • Standard Deviation is the degree to which the values in a data set are spread out with respect to the mean value.

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2. en.wikipedia.org › wiki › VarianceVariance - Wikipedia

   en.wikipedia.org › wiki › Variance

   • Cached

   May 23, 2024 · In probability theory and statistics, variance is the expected value of the squared deviation from the mean of a random variable. The standard deviation (SD) is obtained as the square root of the variance. Variance is a measure of dispersion, meaning it is a measure of how far a set of numbers is spread out from their average value.

3. brilliant.org › wiki › variance-definitionVariance | Brilliant Math & Science Wiki

   brilliant.org › wiki › variance-definition

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   5 days ago · Variance is a statistic that measures how much a random variable deviates from its expected value. Learn how to calculate variance, its properties, and how it relates to standard deviation with examples and formulas.

4. www.geeksforgeeks.org › varianceVariance | Definition, Formula, Examples & Properties

   www.geeksforgeeks.org › variance

   • Cached

   May 21, 2024 · Variance is a measure of how the data is spread with respect to the mean or the average value of the data set. Learn about the types, formulas, properties and examples of variance for population and sample data, and how it relates to standard deviation and covariance.

5. Videos

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     Variance - Clearly Explained (How To Calculate Variance)

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     How To Calculate Variance

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     How To Calculate The Sample Variance | Introduction to Statistics

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6. www.britannica.com › topic › varianceVariance | statistics | Britannica

   www.britannica.com › topic › variance

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   May 9, 2024 · variance, in statistics, the square of the standard deviation of a sample or set of data, used procedurally to analyze the factors that may influence the distribution or spread of the data under consideration. See mean.

   • Author: The Editors of Encyclopaedia Britannica

7. www.investopedia.com › terms › sStandard Deviation Formula and Uses vs. Variance - Investopedia

   www.investopedia.com › terms › s

   • Cached

   May 23, 2024 · What Is Standard Deviation? Standard deviation is a statistical measurement of the dispersion of a dataset relative to its mean. If data points are further from the mean, there is a...

   • Author: Marshall Hargrave

   • Video Duration: 2 min

8. www.analyticsvidhya.com › blog › 2021Descriptive Statistics : A Comprehensive Guide - Analytics Vidhya

   www.analyticsvidhya.com › blog › 2021

   • Cached

   2 days ago · Measures of Dispersion: Variance, standard deviation, and range help us understand the spread or variability of the data. Visualizations: Creating graphs, histograms, bar charts, and pie charts visually represent the data’s distribution and characteristics. Types of Statistics.

9. en.wikipedia.org › wiki › Standard_deviationStandard deviation - Wikipedia

   en.wikipedia.org › wiki › Standard_deviation

   • Cached

   3 days ago · In statistics, the standard deviation is a measure of the amount of variation of a random variable expected about its mean. [1] . A low standard deviation indicates that the values tend to be close to the mean (also called the expected value) of the set, while a high standard deviation indicates that the values are spread out over a wider range.