# What is the variance of {-13, 10, 8, -3, 6, 12, 7}?

Dec 18, 2015

Depending upon whether the given data is to be taken as the entire population (all values) or a sample from some larger population:
Population variance ${\sigma}^{2} \cong 66.7$
Sample variance ${s}^{2} \cong 77.8$

#### Explanation:

This can be determined using standard built-in functions of a scientific calculator or a spread sheet (as below):

...or it may be calculated in steps as:

1. Determine the sum of the data values
2. Divide the sum of the data values by the number of data values to obtain the mean
3. For each data value subtract the mean* from the data value to obtain the deviation from the mean**
4. Determine the sum of the deviations of the data values from the mean.

For population variance:

1. Divide the sum of the deviations by the number of data values* to obtain the population variance**.

For sample variance

1. Divide the sum of the deviations by 1 less than the number of data values to obtain the sample variance