# What is the variance of {-4, 3, 12, 9, 10, -1, 0}?

##### 1 Answer

Population variance:

Sample variance:

#### Explanation:

The answer depends upon whether the data given is intended to be the entire population or a sample from the population.

In practice we would simply use a calculator, spreadsheet, or some software package to determine these values. For example, an Excel spreadsheet might look like:

(note that column F is only intended to document the builtin functions used in column D)

Since this exercise is probably intended to be about how variance might be calculated without direct mechanical/electronic means, the following spreadsheet compromises by showing the essential components of such a calculation:

Calculations:

- The **mean** (average) of the data values (sum divided by number of data values).

- The **deviation** of each data value from the mean

- The square of each deviation from the mean

- The sum of the squares of the deviations

For **Population Variance**

- The sum of the squares of the deviations is divided by the number of data values.

For **Sample Variance**

- The sum of the squares of the deviations is divided by **1 less than** the number of data values