Our friend says that if two data sets have the same range we can assume that the data sets have the same standard deviation, because both of them are measures of variation. Let's first recall the formulas for both measures of variation.
Observing the formulas, we can see that the range tells us over how many numbers the data extends, a bit like measuring its width. Conversely, the standard deviation measures how far values are from the mean. Although both measures tell us how the data is spread out, the way they are calculated is entirely different. Therefore, our friend is incorrect.
