Question

True or false:

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

Answer 1

False. Consider the distriubtion with a mean of 1000, then 10000 data points between 99.9 and 100.1, and a data point at zero, and one at a thousand. Its standard deviation is very small compared to
a mean of 100, 40 datapoints between 80 and 120, the standard deviation will be larger than the first, even if its range is smaller.

Answer 2

Thanks, Bob. The explanation helps!

Answer 3

true