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If Q is a set of consecutive integers, what is the standard

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If Q is a set of consecutive integers, what is the standard [#permalink] New post 02 Jul 2011, 12:43
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If Q is a set of consecutive integers, what is the standard deviation of Q?

(1) Set Q contains 21 terms.

(2) The median of set Q is 20.
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Re: Standard deviation problem [#permalink] New post 02 Jul 2011, 14:05
ruturaj wrote:
If Q is a set of consecutive integers, what is the standard deviation of Q?

(1) Set Q contains 21 terms.

(2) The median of set Q is 20.


st 2. median = 20
set = {19,20,21} or set = {18,19,20,21,22} => different deviations...so not sufficient

st 1 : set has 21 elements...so my median = mean = a22/2 = a11

for deviation formula is (sum of|ai-mean|)/n

here we know n=21
mean = a10
since they are consecutive integers |a1-a2|=1
so we |a11-a1|=10 similiarly all deciations can be found...squared and divided...so we will get a proper answer...therefore statement 1 is conclusive and sufficient!

hope it helps

also, study the Gmatclub notes on standard deviation in Gmat book
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Re: Standard deviation problem [#permalink] New post 02 Jul 2011, 22:33
please let me know the link for standard deviation probs

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Re: Standard deviation problem [#permalink] New post 03 Jul 2011, 02:26
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gmatclub(dot)com/forum/gmat-math-book-87417(dot)html

i have placed unwanted (dot)s in between cuz i cant post links...havent been a member for five days...but thats the address for the open source book....go to the standard deviation section...very nice...all inclusive...you wont need to refer a second source.
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Re: Standard deviation problem [#permalink] New post 03 Jul 2011, 03:57
If you know all of the distances within a set, you can always find its standard deviation, since standard deviation is only based on the distances from each element to the average. So if you have a set of 21 consecutive integers, you can always find the standard deviation; you don't need to know how big these integers are.

If it's not clear why that's true, you can let M be the average of your 21 consecutive integers (M is also the median since our set is equally spaced). Then your set is:

M-10, M-9, M-8, ..., M-1, M, M+1, ..., M+8, M+9, M+10

and you can see that we know all of the distances from each element to M; those distances are 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, and 10. Those are the numbers you need to compute standard deviation.
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Re: Standard deviation problem [#permalink] New post 04 Jul 2011, 23:26
fivedaysleft,

Can you please explain statement1 again?
mean = a22/2 = a11

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Re: Standard deviation problem [#permalink] New post 05 Jul 2011, 05:22
it means that in an ordered set the mean is always the middle number
ie for a set with 21 elements, the middle element is the (21+1)/2 element ie a11

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Re: Standard deviation problem [#permalink] New post 05 Jul 2011, 05:51
fivedaysleft wrote:
it means that in an ordered set the mean is always the middle number
ie for a set with 21 elements, the middle element is the (21+1)/2 element ie a11


You mean to say that in an 'equally spaced' set, the mean and median are equal. There's no such thing as an 'ordered set'; sets are not in any order (if a list of numbers is in order, it's a sequence, not a set).
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Re: Standard deviation problem [#permalink] New post 05 Jul 2011, 06:10
ruturaj wrote:
If Q is a set of consecutive integers, what is the standard deviation of Q?

(1) Set Q contains 21 terms.

(2) The median of set Q is 20.


Statement 1) sufficient, 21 terms known, stdev can be found (no need to calculate)
Statement 2) no of terms not known, not sufficient

A
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Re: Standard deviation problem [#permalink] New post 05 Jul 2011, 06:15
IanStewart wrote:
fivedaysleft wrote:
it means that in an ordered set the mean is always the middle number
ie for a set with 21 elements, the middle element is the (21+1)/2 element ie a11


You mean to say that in an 'equally spaced' set, the mean and median are equal. There's no such thing as an 'ordered set'; sets are not in any order (if a list of numbers is in order, it's a sequence, not a set).


acknowledged. My bad :)
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Re: Standard deviation problem [#permalink] New post 07 Jul 2011, 06:26
To find SD we need Set where we can find mean and then calculate SD

So A is sufficient. B has no relation with median
Re: Standard deviation problem   [#permalink] 07 Jul 2011, 06:26
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