# What is the variance of the following set of numbers?: {12, 19,19, 19, 20, 20, 21, 21, 21, 22, 22, 22, 22, 22, 22,23, 23, 23, 24, 25, 26, 26, 27, 27, 28, 32}

Nov 24, 2015

Variance (Population): ${\sigma}^{2} \approx 20.9$

#### Explanation:

Population Variance (color(black)(sigma^2) is the average of the the squares of the differences between each population data item and the population mean.

For a population $\left\{{d}_{1} , {d}_{2} , {d}_{3} , \ldots\right\}$ of size $n$
with a mean value of $\mu$

${\sigma}^{2} = \frac{\sum {\left({d}_{i} - \mu\right)}^{2}}{n}$