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median mean and range correlation

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Manager
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Joined: 25 Aug 2011
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GMAT 1: 730 Q49 V40
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median mean and range correlation [#permalink] New post 02 Mar 2012, 22:44
Set S consists of positive numbers. If -1 is added as an element to set S, which of the following is impossible ?

The mean will decrease but median will not change.
The median will decrease but mean will not change.
The range will increase but median will not change.
The range will increase but mean will decrease.
The standard deviation will increase but mean will decrease.

what is the best way to test this.. Am getting bogged down by picking numbers .. Also on picking numbers am unable to decide between A B and C - all seem impossible. Pl help
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Re: median mean and range correlation [#permalink] New post 02 Mar 2012, 23:15
Expert's post
devinawilliam83 wrote:
Set S consists of positive numbers. If -1 is added as an element to set S, which of the following is impossible ?

The mean will decrease but median will not change.
The median will decrease but mean will not change.
The range will increase but median will not change.
The range will increase but mean will decrease.
The standard deviation will increase but mean will decrease.

what is the best way to test this.. Am getting bogged down by picking numbers .. Also on picking numbers am unable to decide between A B and C - all seem impossible. Pl help


The mean of set S is sum/n, where n is # of terms in set S.

Since set S consist of positive numbers, then when we add -1 to the set the sum of the numbers in the new set will decrease. So, the new mean will be (less sum)/(more terms)=(less sum)/(n+1), which will be less than the sum/n. Hence the mean must decrease.

Answer: B.

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Re: median mean and range correlation   [#permalink] 02 Mar 2012, 23:15
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