# What are the variance and standard deviation of {1, 1, 1, 1, 1, 80, 1, 1, 1, 1, 1, 1}?

##### 1 Answer

The population variance is:

and the populations standard deviation is the square root of this value:

#### Explanation:

First, let's assume that this is the entire population of values. Therefore we are looking for the **population variance **. If these numbers were a set of samples from a larger population, we would be looking for the **sample variance ** which differs from the population variance by a factor of

The formula for the population variance is

where

In our population the mean is

Now we can proceed with the variance calculation:

and the standard deviation is the square root of this value: