Quentin Johnson

2022-01-19

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

Samantha Brown

Expert

Standard deviation (population): ${\sigma }_{pop}=1$
Explanation:
The mean is clearly 2
Each value deviates from the mean by $±1$
So the square of each value's deviation from the mean is 1 and the average of the squared deviations (i.e. the variance, ${\sigma }_{pop}^{2}$) is 1
Therefore the standard deviation (assuming the data represents the entire population) is ${\sigma }_{pop}=\sqrt{1}=1$

Do you have a similar question?