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

Dec 10, 2015

Population variance: ${\sigma}_{\text{pop.}}^{2} \cong 32.98$
Sample variance: ${\sigma}_{\text{sample}}^{2} \cong 38.48$

#### 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