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SIR, I IS IT TRUE THAT S.D IS < OR EQUAL TO RANGE/2 ( HALF OF RANGE) ?Ian Stewart wrote:We want to know which set has the greater standard deviation - that is, we want to know in which set the elements tend to be further from the mean. We don't care at all how big the mean is; we only care how far away elements are from the mean. So Statement 2 here is completely useless.
Statement 1 is also not sufficient. The range of a set only takes into account two elements: the largest and the smallest. The standard deviation, on the other hand, is based on the distances from *every* element to the mean. If you take the two sets below:
A = {0, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 100}
and
B = {1, 1, 1, 1, 1, 1, 50, 99, 99, 99, 99, 99, 99}
the first set has a greater range than the second set. But because most of the elements in set A are clustered around the mean, while most of the elements in set B are far from the mean, set A will have a much smaller standard deviation than set B.
The answer is E.
Yes, that is true. It is not something you will *ever* need to use on the GMAT (if you think that fact is needed on a GMAT question, you've misunderstood something). That relationship is also irrelevant for the question above - I don't see why you think it makes statement 1 sufficient, so I can't help more than that.[email protected] wrote:
SIR, I IS IT TRUE THAT S.D IS < OR EQUAL TO RANGE/2 ( HALF OF RANGE) ?
IF THIS IS TRUE THAN WHY WE CAN'T ANSWER THIS BY USING STATEMENT A
PLEASE HELP , HELP
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