# What is the standard deviation of {1, 1, 1, 3, 3, 3}?

Dec 13, 2015

Standard deviation (population): ${\sigma}_{\text{pop.}} = 1$

#### Explanation:

The mean is clearly $2$

Each value deviates from the mean by $\pm 1$
So the square of each value's deviation from the mean is $1$

and the average of the squared deviations (i.e. the variance, ${\sigma}_{\text{pop.}}^{2}$) is 1

Therefore the standard deviation (assuming the data represents the entire population) is ${\sigma}_{\text{pop.}} = \sqrt{1} = 1$