# What are the variance and standard deviation of {1, -1, -0.5, 0.25, 2, 0.75, -1, 2, 0.5, 3}?

##### 1 Answer

If the given data is the entire population then:

If the given data is a sample of the population then

#### Explanation:

To find the variance (

- Find the sum of the population values
- Divide by the number of values in the population to obtain the
**mean** - For each population value calculate the difference between that value and the mean then square that difference
- Calculate the sum of the squared differences
- Calculate the population variance (
#sigma_"pop"^2# ) by dividing the sum of the squared differences by the number of population data values. - Take the (primary) square root of the population variance to obtain the population standard deviation (
#sigma_"pop"# )

If the data represents only a sample extracted from a larger population then you need to find the sample variance (

The process for this is identical **except** in step 5 you need to divide by

It would be unusual to to all of this by hand. Here's what it would look like in a spreadsheet: