Population Variance and Sample Variance
The table gives the differences between the population variance and sample variance:
Population Variance | Sample Variance |
|---|---|
Population variance is calculated using the entire data set. | Sample variance is calculated using only a sample of the data set. |
You calculate the population variance when the dataset you’re working with, represents an entire population, i.e. every value that you’re interested in. | You calculate the sample variance when the dataset you’re working with represents a a sample taken from a larger population of interest. |
The formula to calculate population variance is: [Tex]σ^2 =\dfrac{ Σ (x_i – μ)^2} N[/Tex] where:
| The formula to calculate sample variance is: [Tex]s^2 =\dfrac{ Σ (x_i – x)^2}{(n-1)}[/Tex] where:
|
Population Variance
Population variance is a fundamental concept in statistics that quantifies the average squared deviation from the mean of a set of data points in a population. It is a measure of how spread out a group of data points is.
There are two types of data available, namely, ungrouped and grouped data. Thus, there are two formulas to calculate the population variance. In this article, we will learn more about population variance, its formulas, and various associated examples.
Table of Content
- What is Population Variance?
- Formula of Population Variance
- Ungrouped Data
- Grouped Data
- Population Variance and Sample Variance
- Population Variance and Standard Deviation
- Solved Problems on Population Variance
- Practice Questions on Population Variance
- FAQs on Population Variance