median

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ketkoag: Legendary Member; Posts: 876; Joined: Thu Apr 10, 2008 8:14 am; Thanked: 13 times

by ketkoag » Wed Jun 10, 2009 12:54 am

If 2 numbers are picked out from 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, what's the deviation of the remaining numbers?
1) The median of the remaining numbers is 10
2) The average value doesn't change

[spoiler]IMO : D, please confirm the answer..[/spoiler]

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Source: Beat The GMAT — Data Sufficiency | Wed Jun 10, 2009 12:54 am

iamcste: Legendary Member; Posts: 940; Joined: Tue Aug 26, 2008 3:22 amFollowed by: 1 member; Thanked: 55 times

Re: median

by iamcste » Wed Jun 10, 2009 1:24 am

ketkoag wrote:If 2 numbers are picked out from 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, what's the deviation of the remaining numbers?
1) The median of the remaining numbers is 10
2) The average value doesn't change

[spoiler]IMO : D, please confirm the answer..[/spoiler]

yes IMO D

d=constant difference=2, mean=median

1. this means 1 and 19 are out to get median 10.. for the remaining nos, we can find standard deviation as we know data set as well as the mean( =median)

2. Current average=10..even after removing 2 integers, average=10

Also as mean=median...this statement can be rephrased to statment "The median of the remaining numbers is 10"

Sufficient

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ketkoag: Legendary Member; Posts: 876; Joined: Thu Apr 10, 2008 8:14 am; Thanked: 13 times

by ketkoag » Wed Jun 10, 2009 2:26 am

thanks

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tohellandback: Legendary Member; Posts: 752; Joined: Sun May 17, 2009 11:04 pm; Location: Tokyo; Thanked: 81 times; GMAT Score:680

by tohellandback » Wed Jun 10, 2009 6:20 am

I think the answer should be E

in both the cases we can remove any of the 5 pairs of numbers and it satisfies the condition but it will change the standard deviation.

Thanks

The powers of two are bloody impolite!!

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mikeCoolBoy: Master | Next Rank: 500 Posts; Posts: 119; Joined: Tue Jan 20, 2009 10:16 pm; Thanked: 9 times; GMAT Score:730

by mikeCoolBoy » Wed Jun 10, 2009 10:23 am

I agree with tohellandback

the mean for the initial set is 10 = (1+19)/2

1) says that the new mean is 10
you can remove the pairs (1,19), (3,17), (5,15) ... and the mean is 10 but the standard deviation changes

2) if you remove the any of the pairs I mentioned you get the same mean but the standard deviation changes.

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