# What are the variance and standard deviation of {2,9,3,2,7,7,12}?

##### 1 Answer

Variance (population):

Standard Deviation (population):

#### Explanation:

The Sum of the data values is

The Mean (

For each of the data values we can calculate the difference between the data value and the mean and then square that difference.

The sum of the squared differences divided by the number of data values gives the population variance (

The square root of of the population variance gives the population standard deviation (

**Note:** I've assumed the data values represent the *entire population*.

If the data values are only a *sample* from a larger population then you should calculate the **sample variance**, **sample standard deviation**,

**Note 2:** Normal statistical analysis is done with the aid of computers (e.g. using Excel) with built-in functions to provide these values.