Question

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

Answer 1

Population Variance: `sigma_("pop.")^2 = 157.92`
Sample Variance: `s_("pop.")^2 = 183.24`

Explanation:

Variance is calculated based on
the sum of
`color(white)("XXX")`the squares of
`color(white)("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: