# What is the variance of the following numbers?: 11, 23, 45, 42, 39, 56, 51, 17, 22, 29, 46, 33, 38, 33, 31,

Dec 2, 2015

Assuming we are looking for a population variance:
${\textcolor{w h i t e}{\text{XXX")sigma_("pop}}}^{2} = 150.64$

#### Explanation:

Here is the data in a spreadsheet format (of course, with the given data, there are spreadsheet or calculator functions to give the variance without the intermediate values; they are here for instructional purposes only).

The Population Variance is
(the sum of the squares of the differences of the individual data values from the mean)
$\textcolor{w h i t e}{\text{XXX}}$divided by
(the number of data values)

Not that if the data was intended to be only a sample from some larger population then you should calculate the "Sample Variance" for which the division is by (one less than the number of data values).