What is the variance of {8, 19, 10, 0, 1, 0}?

${\sigma}^{2} = \frac{428}{9} = 47.5556$

Explanation:

From the given: $n = 6$

We solve for arithmetic mean first.

$\overline{x} = \frac{8 + 19 + 10 + 0 + 1 + 0}{6} = \frac{38}{6} = \frac{19}{3}$

The formula for variance of ungrouped data is

${\sigma}^{2} = \frac{\sum {\left(x - \overline{x}\right)}^{2}}{n}$

${\sigma}^{2} = \frac{{\left(8 - \frac{19}{3}\right)}^{2} + {\left(19 - \frac{19}{3}\right)}^{2} + {\left(10 - \frac{19}{3}\right)}^{2} + {\left(0 - \frac{19}{3}\right)}^{2} + {\left(1 - \frac{19}{3}\right)}^{2} + {\left(0 - \frac{19}{3}\right)}^{2}}{6}$

${\sigma}^{2} = \frac{428}{9} = 47.5556$

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