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

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Dec 16, 2015

Population Variance: $σ_{pop.}^{2} = 157.92$ $sigma_("pop.")^2 = 157.92$
Sample Variance: $s_{pop.}^{2} = 183.24$ $s_("pop.")^2 = 183.24$

Explanation:

Variance is calculated based on
the sum of
$XXX$ $color(white)("XXX")$ the squares of
$XXXXXX$ $color(white)("XXXXXX")$ 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 $σ^{2}$ $sigma^2$ 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 $s^{2}$ $s^2$ 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:
enter image source here

Or step-by-step:
enter image source here

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