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Re: Standard deviation problem [#permalink]
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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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]
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:

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. _________________

Nov 2011: After years of development, I am now making my advanced Quant books and high-level problem sets available for sale. Contact me at ianstewartgmat at gmail.com for details.

Re: Standard deviation problem [#permalink]
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

my GMAT was today. got shredded in verbal. 34 quants was decent 48 680 in all _________________

It matters not how strait the gate, How charged with punishments the scroll, I am the master of my fate : I am the captain of my soul. ~ William Ernest Henley

Re: Standard deviation problem [#permalink]
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). _________________

Nov 2011: After years of development, I am now making my advanced Quant books and high-level problem sets available for sale. Contact me at ianstewartgmat at gmail.com for details.

Re: Standard deviation problem [#permalink]
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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