# What is the variance of {-5, 19, -20, 5, 16, -7, 1}?

Dec 16, 2015

Population Variance: ${\sigma}_{\text{pop.}}^{2} = 157.92$
Sample Variance: ${s}_{\text{pop.}}^{2} = 183.24$

#### Explanation:

Variance is calculated based on
the sum of
$\textcolor{w h i t e}{\text{XXX}}$the squares of
$\textcolor{w h i t e}{\text{XXXXXX}}$the deviations between each data value and the mean of the data values.

If the data values represent the entire population
then we calculate the population variance ${\sigma}^{2}$ by dividing the sum of the squares (above) by the number of data values in the population.

If the data values represent a sample from a larger population
then we calculate the sample variance ${s}^{2}$ by dividing the sum of the squares (above) by (the number of data values minus 1).

We would normally use a spreadsheet or calculator to do this.

Using builtin functions:

Or step-by-step: