The distribution with the largest standard deviation necessarily has the largest range.

Question

Quizplus · Accepted Answer

The range is the difference between the maximum and minimum values in a distribution, while the standard deviation measures the average distance of each data point from the mean. A distribution can have a large standard deviation with a smaller range if the data is spread out around the mean, and another distribution can have a larger range but a smaller standard deviation if most data points are clustered near the mean with only a few extreme values.

The Distribution with the Largest Standard Deviation Necessarily Has the Largest