What is the variance of {-5, 19, -20, 5, 16, -7, 1}?

1 Answer
Dec 16, 2015

Population Variance: #sigma_("pop.")^2 = 157.92#
Sample Variance: #s_("pop.")^2 = 183.24#

Explanation:

Variance is calculated based on
the sum of
#color(white)("XXX")#the squares of
#color(white)("XXXXXX")#the deviations between each data value and the mean of the data values.

If the data values represent the entire population
then we calculate the population variance #sigma^2# by dividing the sum of the squares (above) by the number of data values in the population.

If the data values represent a sample from a larger population
then we calculate the sample variance #s^2# by dividing the sum of the squares (above) by (the number of data values minus 1).

We would normally use a spreadsheet or calculator to do this.

Using builtin functions:
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Or step-by-step:
enter image source here