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A set of data consists of the following 5 numbers: 0,2,4,6, [#permalink]
15 Jul 2008, 08:41

50. A set of data consists of the following 5 numbers: 0,2,4,6, and 8. Which two numbers, if added to create a set of 7 numbers, will result in a new standard deviation that is close to the standard deviation for the original 5 numbers?

A). -1 and 9 B). 4 and 4 C). 3 and 5 D). 2 and 6 E). 0 and 8

D is closest I hope this one is not a GMAT/GMATPrep material as I see no short cut for it. ***EDIT**** WHAT IS THE SOURCE OF THIS QUESTION? I hope not GPrep!

Last edited by mbawaters on 15 Jul 2008, 10:33, edited 2 times in total.

Re: standard deviation [#permalink]
15 Jul 2008, 11:49

i say B. rem formula of S.D from the formula, higher S.D means that higher is the spread. so by adding 4 and 4, the spread does not increase(since the mean is 4), at the same time, as we are increasing the no. of samples(from 5 to 7), the denominator in the formula (N) increases, thereby decreasing the S.D. its an old problem....

Re: standard deviation [#permalink]
15 Jul 2008, 11:55

arjtryarjtry wrote:

i say B. rem formula of S.D from the formula, higher S.D means that higher is the spread. so by adding 4 and 4, the spread does not increase(since the mean is 4), at the same time, as we are increasing the no. of samples(from 5 to 7), the denominator in the formula (N) increases, thereby decreasing the S.D. its an old problem....

Yeah but you'r now dividing it by 7 instead of 5...

Re: standard deviation [#permalink]
16 Jul 2008, 07:43

1

This post received KUDOS

Expert's post

My fast approach to SD. (10-20sec)

Think of SD as average deviation of data from a mean. the closer deviations to SD we add the less we change SD. 0,2,4,6,8 has mean of 4 and average deviation of 2. Therefore, 6 and 2 add the least changes in SD: 2=(6-4) and 2=(4-2). So, D _________________

Re: standard deviation [#permalink]
16 Jul 2008, 07:52

walker wrote:

My fast approach to SD. (10-20sec)

Think of SD as average deviation of data from a mean. the closer deviations to SD we add the less we change SD. 0,2,4,6,8 has mean of 4 and average deviation of 2. Therefore, 6 and 2 add the least changes in SD: 2=(6-4) and 2=(4-2). So, D

walker can you ellaborate? knowing that 'SD is a deviation of data from a mean' how did you reject '4 and 4' when mean is 4? Thanks

Re: standard deviation [#permalink]
16 Jul 2008, 08:58

walker wrote:

My fast approach to SD. (10-20sec)

Think of SD as average deviation of data from a mean. the closer deviations to SD we add the less we change SD. 0,2,4,6,8 has mean of 4 and average deviation of 2. Therefore, 6 and 2 add the least changes in SD: 2=(6-4) and 2=(4-2). So, D

D is closest I hope this one is not a GMAT/GMATPrep material as I see no short cut for it. ***EDIT**** WHAT IS THE SOURCE OF THIS QUESTION? I hope not GPrep!

I picked up this Q from a compilation of tough Qs that have appeared on GMAT ..There is a document that another friend of mine had given me.M not sure whether these really appeared on GMAT but i just do them when i don't feel like doing verbal .. I am not sure whether i can attach the file on this forum ... The explanation given there is something like this SD =Sqrt (sum (X-x)^2 /N) Since N is changing from 5 to 7 . Value of sum(X-X)^2 should change from 40 (current) to 48. So that SD remains same.

Re: standard deviation [#permalink]
16 Jul 2008, 11:59

Expert's post

mbawaters wrote:

walker can you ellaborate? knowing that 'SD is a deviation of data from a mean' how did you reject '4 and 4' when mean is 4? Thanks

MamtaKrishnia wrote:

Walker how did u calculate the avg SD to be 2

I would say that this problem cannot be solved in a such way, because really deviation is 3 (2 was my mistake) and we have two close answer: D and E. see here for another approach: 7-t58976 _________________

Re: standard deviation [#permalink]
17 Jul 2008, 04:33

scthakur wrote:

MamtaKrishna,

It should change to 56. But answer choice D gives the change to 48 that is closest to 56.

Thanks scthakur, This makes sense to me.

Walker , In the other link you have posted one plausible explanation for this Q ... A. D(SET 5, -1, 9) = 3.5857 B. D(SET 5, 4, 4) = 2.3905 C. D(SET 5, 3, 5) = 2.4495 D. D(SET 5, 2, 6) = 2.6186 ---D(SET 5) = 2.8284 E. D(SET 5, 0, 8) = 3.2071

Re: standard deviation [#permalink]
17 Jul 2008, 06:42

MamtaKrishnia wrote:

Walker , In the other link you have posted one plausible explanation for this Q ... A. D(SET 5, -1, 9) = 3.5857 B. D(SET 5, 4, 4) = 2.3905 C. D(SET 5, 3, 5) = 2.4495 D. D(SET 5, 2, 6) = 2.6186 ---D(SET 5) = 2.8284 E. D(SET 5, 0, 8) = 3.2071

I didnt get this explanation

His explanation was not that one (this is just a numerical approach with a computer: you cannot do it during the GMAT), but that one:

walker wrote:

D

\(x_{av}=(0+2+4+6+8)/5=4\)

\((\sum{(x-x_{av})^2})_{av}=(16+4+0+4+16)/5=8\)

for all variants \(y_{av}=4\) Ideally, we have to add two numbers for which\((\sum{(y-y_{av})^2})_{av}=8\)

D has the closest value - 4.

I did the same above and developped it a bit:

Oski wrote:

Compute standard deviation s of the original 5 :

\(s^2 = \frac{4^2+2^2+0+2^2+4^2}{5} = 8\)

You want to add two new numbers and want \(s^2\) to stay close of 8.

New \(s^2\) will be : \(s^2 = \frac{8*5+2*(X-4)^2}{7}\) (since 4 remains the average of the new set whichever choice you pick)

So if we want it to remain close to 8 we want to be close to \(\frac{8*5+2*(X-4)^2}{7} = 8\)

This leads to \((X-4)^2 = 8\) and thus \(X = 4 + 2 sqrt(2)\) or \(X = 4 - 2 sqrt(2)\)

\(sqrt(2)\) is close to 1.4, so we want X as close to 1.2 or 6.8 ==> answer (D)

Last edited by Oski on 17 Jul 2008, 06:43, edited 1 time in total.

Re: standard deviation [#permalink]
17 Jul 2008, 06:43

Expert's post

MamtaKrishnia wrote:

Walker , In the other link you have posted one plausible explanation for this Q ... A. D(SET 5, -1, 9) = 3.5857 B. D(SET 5, 4, 4) = 2.3905 C. D(SET 5, 3, 5) = 2.4495 D. D(SET 5, 2, 6) = 2.6186 ---D(SET 5) = 2.8284 E. D(SET 5, 0, 8) = 3.2071

I didnt get this explanation

It is not my explanation, it is rather Excel proof that D is a right answer. My explanation here in another post of the thread: p424757#p424757 _________________

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