Which data set has zero standard deviation?

Which data set has zero standard deviation?

• A. 1,1,2,2
• B. 2,2,2,2
• C. 0,0,0,0
• D. 2,2,3,3

Answer: (B)

Standard deviation measures how far data points spread from the average. If every value in a dataset is the same, there is no spread at all, so the standard deviation is zero. In the dataset where every observation is 2, each value equals the mean, so all deviations are zero and the standard deviation is zero. The same happens in the dataset where every observation is 0—the mean is 0 and every value matches it, giving zero deviation. Datasets that mix different numbers have some spread, so their standard deviation is greater than zero.

Standard deviation measures how far data points spread from the average. If every value in a dataset is the same, there is no spread at all, so the standard deviation is zero.

In the dataset where every observation is 2, each value equals the mean, so all deviations are zero and the standard deviation is zero. The same happens in the dataset where every observation is 0—the mean is 0 and every value matches it, giving zero deviation.

Datasets that mix different numbers have some spread, so their standard deviation is greater than zero.