# Variance

In these lessons, we will learn

- Population Variance
- Sample Variance
- Alternate Formulas or Computational Formulas for Variance

Related Topics:

More Statistics Lessons
## Population Variance

The variance is the average of the squared deviations about the mean for a set of numbers. The population variance is denoted by . It is given by the formula:

The capital Greek letter sigma is commonly used in mathematics to represent a summation of all the numbers in a grouping.

*N* is the number of terms in the population.

The following video shows how to calculate the variance of a population.

Variance as a measure of, on average, how far the data points in a population are from the population mean.

Population variance and standard deviation.

How to calculate the variance and standard deviation.

## Sample Variance

The sample variance is denoted by *s*^{2}. The main use for sample variances is as estimators of population variances. The computation of the sample variance differs slightly from computation of the population variance. The sample variance uses *n* – 1 in the denominator instead of *n* because using *n *in the denominator of a sample variance results in a statistic that tends to underestimate the population variance. (This is further explained in the video below)

The formula for sample variance is:

The following video shows how to use the variance of a sample to estimate the variance of a population.

The following video gives the formula and show one example of finding the sample variance.

## Alternate Formulas or Computational Formulas for Variance

Sometimes, books may give different formulas for variance.

We will now show how to derive these different formulas for variance.

The following video will describe how to derive the different alternate formulas for variance.

Finding the sample standard deviation using the computation formula.

You can use the Mathway widget below to practice Algebra or other math topics. Try the given examples, or type in your own problem. Then click "Answer" to check your answer.