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# A set of data consists of the following 5 numbers: 0,2,4,6,

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Director
Joined: 08 Jun 2007
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Kudos [?]: 79 [0], given: 0

A set of data consists of the following 5 numbers: 0,2,4,6, [#permalink]  26 Nov 2007, 20:09
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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

I know the solution but I just didn't like . Looking for nice and easy approach or link if this was posted earlier.
CEO
Joined: 17 Nov 2007
Posts: 3578
Concentration: Entrepreneurship, Other
Schools: Chicago (Booth) - Class of 2011
GMAT 1: 750 Q50 V40
Followers: 407

Kudos [?]: 2149 [0], given: 359

Expert's post
D.

av=(0+2+4+6+8)/5=4

remember that d=(x-xav)^2 is a key part of standard deviation.

d e {16,4,0,4,16} sd^2=40/5=8

A) -1 and 9 - d=25;25 is too large.
B) 4 and 4 - d=0;0 is too small.
C) 3 and 5 - d=1;1 is too small.
D) 2 and 6 - d=4;4 is possible. sd^2=48/7~7 - the closest.
E) 0 and 8 - d=16;16 is possible. sd^2=72/7~10

Maybe the solution is not so easy. what's OA?
SVP
Joined: 29 Aug 2007
Posts: 2497
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walker wrote:
D.

av=(0+2+4+6+8)/5=4

remember that d=(x-xav)^2 is a key part of standard deviation.

d e {16,4,0,4,16} sd^2=40/5=8

A) -1 and 9 - d=25;25 is too large.
B) 4 and 4 - d=0;0 is too small.
C) 3 and 5 - d=1;1 is too small.
D) 2 and 6 - d=4;4 is possible. sd^2=48/7~7 - the closest.
E) 0 and 8 - d=16;16 is possible. sd^2=72/7~10

Maybe the solution is not so easy. what's OA?

depends how you divide the sum of square dev.

if by n, then E.
if by (n-1), then D.

not sure whaat we use in gmat. imo, for small samples (less than 30), we should use (n-1). so D.
CEO
Joined: 17 Nov 2007
Posts: 3578
Concentration: Entrepreneurship, Other
Schools: Chicago (Booth) - Class of 2011
GMAT 1: 750 Q50 V40
Followers: 407

Kudos [?]: 2149 [0], given: 359

Expert's post
GMAT TIGER wrote:
depends how you divide the sum of square dev.

You are absolutely right. I know that but n is the case of GMAT. I've refreshed my knowledge about standard deviation just before put solution.
(p.115-116 in OG 11th edition.)
......
The other difference of "GMAT logic" from normal one is ignoring densities of materials in solution/mixture problems....
CEO
Joined: 17 Nov 2007
Posts: 3578
Concentration: Entrepreneurship, Other
Schools: Chicago (Booth) - Class of 2011
GMAT 1: 750 Q50 V40
Followers: 407

Kudos [?]: 2149 [0], given: 359

Expert's post
GMAT TIGER wrote:
if by n, then E.
if by (n-1), then D.

rather

if by n, then D.
if by (n-1), then E.

sd^2=40/4=10

4) 48/6=8

5) 72/6=12 - the closest.
Director
Joined: 09 Aug 2006
Posts: 766
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Kudos [?]: 69 [0], given: 0

Re: PS - Standard Deviation [#permalink]  26 Nov 2007, 23:13
ashkrs wrote:
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

I know the solution but I just didn't like . Looking for nice and easy approach or link if this was posted earlier.

You can calculate the variance for the original set and then the variance for the new set to determine that D is the answer.

However, how do you solve this without calculating the variance?
Re: PS - Standard Deviation   [#permalink] 26 Nov 2007, 23:13
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