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by sl750 » Thu Sep 08, 2011 11:50 am
I took a small set of numbers

A-{1,3,3,7} Range=6
B-{1,3,3,5} Range=4

Avg of A = 3.5; Avg of B = 3. Just by eyeballing the respective averages and the elements of their respective sets, we can see that A has a higher SD

Take another case
A-{1,1,1,7} Range=6
B-{1,4,4,5} Range=4

Avg of A = 2.5; Avg of B = 3.5. I took a case with set B having a higher average. In this case too, we see that set A has a higher SD. So sufficient

Statement 2 is not sufficient. As we can see in statement 1, the second example shows that in-spite of set A having a lower average, the SD was larger. So basically, it depends on how far from the mean
the elements of the set are. The farther apart the elements are from the mean, the greater is the SD
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by prateek_guy2004 » Thu Sep 08, 2011 1:19 pm
What do we need to find standard deviation?
Mean and Range

Statement 1 suff

statement 2 insuff

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by [email protected] » Thu Sep 08, 2011 1:40 pm
LIKE YOUR COMMENT BUT ANSWER IS EEEEEE
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by Ian Stewart » Thu Sep 08, 2011 2:06 pm
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.
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by [email protected] » Thu Sep 08, 2011 2:14 pm
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.
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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by Ian Stewart » Thu Sep 08, 2011 4:52 pm
[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
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.
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