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Is the standard deviation of numbers w,x,y and z greater

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Is the standard deviation of numbers w,x,y and z greater [#permalink] New post 10 Aug 2010, 18:43
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Is the standard deviation of numbers w,x,y and z greater than 2?
1) w=3
2) The average of the four numbers is 8
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Re: Is the SD greater than 2 [#permalink] New post 10 Aug 2010, 18:48
(1) w=3 does not say much, insuf
(2) average = 8, so sum of all = 32 insuf

1+2
so sum of x, y, z = 29, does not give me a clue

E
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Re: Is the SD greater than 2 [#permalink] New post 10 Aug 2010, 19:24
E for me too for the same mentioned reasons.
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Re: Is the SD greater than 2 [#permalink] New post 10 Aug 2010, 20:04
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gmatrant wrote:
Is the standard deviation of numbers w,x,y and z greater than 2?
1) w=3
2) The average of the four numbers is 8


You might be able to see intuitively why the answer should be C here - if the average of our four-element set is 8, and one of the elements is equal to 3, then at least one of our elements is pretty far from the mean. That's certainly going to guarantee something about our standard deviation - the standard deviation can't be all that small here.

You can prove that the answer is C, at least if you remember how you find the standard deviation (not something you ever need to calculate on the GMAT, incidentally) - you find the distance from each element to the mean, square those distances, average these squares, then finally take the square root. If our mean is 8, and one of our elements is 3, then one of our distances to the mean is 5. So when we add the squares of the distances, our sum must be at least 5^2 = 25. We now take the average of this sum (so here divide by 4); this average is at least 25/4 = 6.25, and the square root of that is greater than 2.

So if we use both statements, the standard deviation must be greater than 2, and the answer is C.
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Re: Is the SD greater than 2 [#permalink] New post 10 Aug 2010, 21:39
Thanks for the explanation Ian. C is the right answer.
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Re: Is the SD greater than 2 [#permalink] New post 10 Oct 2010, 15:17
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great clue by IanStewart

C

for the set to have a mean of 8 and smallest element to be 3 => sum of other 3 elements = 29 = 8*4 - 3

=> set can be 3, 9, 10, 10 or can have any other 3 number whose sum is 29. whichever those number are, the sum of the difference between those numbers and mean is always 5.

so sd = (5 + 5)/2 = 2.5 > 2
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Re: Is the SD greater than 2   [#permalink] 10 Oct 2010, 15:17
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