Posted by Zodra on Sunday, August 22, 2010 at 6:44am.
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?

statistics  bobpursley, Sunday, August 22, 2010 at 8:30am
1, 1000, 40, 41, 39,40,40,39,41
31,49,74,26,54,36,55,19
Try those. 
statistics  Zodra, Sunday, August 22, 2010 at 1:23pm
@bobpursley thank you very much. I tried those data sets but it didnot work :(

statistics  PsyDAG, Monday, August 23, 2010 at 11:52am
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.