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GMAT PREP Q

This topic has 3 member replies
yvonne12 Master | Next Rank: 500 Posts Default Avatar
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GMAT PREP Q

Post Wed Mar 07, 2007 3:16 pm
A CERTAIN LIST OF 100 DATA HAS AN AVERAGE OF 6 AND A STANDARD DEVIATION OF D WHERE D IS POSITIVE . WHICH OF THE FOLLOWING PAIRS OF DATE, WHEN ADED TO THE LIST , MUST RESULT IN A LIST OF 102 DATA W STANDARD DEVIATION LESS THAN D?
-6 AND 0
0 AND 0
0 AND 6
0 AND 12

PLEASE EXPLAIN

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yvonne12 Master | Next Rank: 500 Posts Default Avatar
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Post Wed Mar 07, 2007 9:15 pm
You're right. I accidentally left out 6 and 6. JAyhawk...you're so smart Wink

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jayhawk2001 Community Manager
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Post Wed Mar 07, 2007 7:43 pm
Adding 2 numbers to the list actually changes the average unless both
numbers are 6. We don't have an option (6 and 6) but lets assume that
the average is in the vicinity of 6 (atleast looking at the choices).

Since SD = sum (square (x - avg)) / N, we need to choose the numbers
that have the least value for square (x - avg).

If we consider the average as unchanged, the numbers that yield the
least sum = 0 and 6. This would cause the numerator to increase by
just 36.

-6 and 0 increases sum by 140
0 and 0 increases sum by 72
0 and 6 increases sum by 36
0 and 12 increases sum by 72

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ssiva Junior | Next Rank: 30 Posts Default Avatar
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Post Wed Mar 07, 2007 4:25 pm
I am not sure but is it 0 and 0 ?
as sum( sqaures of ( x-x' ) ) for 0 and 0 is the lowest.

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