ern5231 wrote:it's a gmatprep question!
As written, it cannot possibly be a GMATPrep question. No matter what two elements are removed from the list, the standard deviation must change (though it takes some work to prove that). So you do not need either of the statements to know that the answer to the question must be 'yes'. I could imagine the question asking whether the standard deviation increases, but not whether the standard deviation 'remains unchanged'.
adilka wrote:Should be E.
Here are 3 ways to remove numbers and keep both (1) and (2) unchanged.
1) remove 1 and 19
2) remove 9 and 11
3) remove 7 and 13
The last 2 mess up the dispersion around the mean, which is what st. def. measures
The 1st one doesn't mess up the dispersion (i think, please confirm), hence ST,DEV unchanged.
There are actually five ways to remove pairs of elements without affecting the mean or median - you could remove 1 and 19, 3 and 17, 5 and 15, 7 and 13 or 9 and 11. In each case the standard deviation will change; note that when computing the standard deviation, you average the sums of the squares of the distances to the mean, so when we change the size of the set, we're averaging by a different number -- in the original set, we average by 10, and after removing two elements, we're averaging by 8. That alone makes it very difficult for two sets of differing sizes to have equal standard deviations unless there is some kind of strong similarity between the sets.
