Construct two different datasets such that the range of the first set is greater than the range of the second set, but the standard deviation of first set is less than the standard deviation of the second set. Can you say that one of your datasets has the smaller variation of the two?

Answer 1

1, 1000, 40, 41, 39,40,40,39,41

31,49,74,26,54,36,55,19

Try those.

Answer 2

@bobpursley thank you very much. I tried those data sets but it didnot work :(

Answer 3

Try 75, 25, 50, 51, 52, 49, 48, 50, 50, 49 for your first equation and

61, 39, 62, 38, 63, 37, 64, 36, 65, 35 for the second.

I have made the distributions with mean = 50 and n = 10 to make the calculations easier for you.

The range only relies on the two most extreme scores, while the SD includes the variation from the mean of all scores.