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# If two numbers are removed from 2, 4, 6, 8, 10, 12, 14, 16,

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Current Student
Joined: 11 May 2008
Posts: 552
If two numbers are removed from 2, 4, 6, 8, 10, 12, 14, 16, [#permalink]

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04 Sep 2008, 03:37
. If two numbers are removed from 2, 4, 6, 8, 10, 12, 14, 16, 18, and 20, what is the standard deviation of the remaining numbers?
(1) The average remains unchanged after the numbers removing.
(2) The median remains unchanged after the numbers removing.

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SVP
Joined: 17 Jun 2008
Posts: 1502
Re: S.D of consecutive nos. [#permalink]

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04 Sep 2008, 03:47
I will go with D.

Since, the numbers are consecutive even numbers, average or median will remain the same only if the two extreme numbers are removed. And, hence, it will be possible to calculate the SD.
Senior Manager
Joined: 16 Jul 2008
Posts: 285
Re: S.D of consecutive nos. [#permalink]

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04 Sep 2008, 04:00
I think E.

We have from the stem that the average is the same as the median and it is 11. We can remove two numbers without changing the median/average, by removing any of the pairs: 2&20, 4&18, 6&16, 8&14, 10&12. I never bothered to remember how stdev is calculated, but if we remove 2 and 20, it will be different than removing 10 and 12, right?
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Last edited by Nerdboy on 05 Sep 2008, 00:31, edited 1 time in total.
SVP
Joined: 17 Jun 2008
Posts: 1502
Re: S.D of consecutive nos. [#permalink]

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04 Sep 2008, 04:59
If you remove 4 and 18 or 6 and 16, the average will change.
SVP
Joined: 17 Jun 2008
Posts: 1502
Re: S.D of consecutive nos. [#permalink]

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04 Sep 2008, 05:00
Oops....my silly mistake.....it will be E.
VP
Joined: 05 Jul 2008
Posts: 1368
Re: S.D of consecutive nos. [#permalink]

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04 Sep 2008, 09:01
Even though average/median remains the same, the SD for a subset of the numbers will be different because the numerators (in calculation of SD) varies. Hence E
VP
Joined: 17 Jun 2008
Posts: 1322
Re: S.D of consecutive nos. [#permalink]

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05 Sep 2008, 22:19
arjtryarjtry wrote:
. If two numbers are removed from 2, 4, 6, 8, 10, 12, 14, 16, 18, and 20, what is the standard deviation of the remaining numbers?
(1) The average remains unchanged after the numbers removing.
(2) The median remains unchanged after the numbers removing.

When we symmetrically remove the data the mean and median remain unchanged but SD is distance from the mean hence which values removed does matter here !!!Hence in both the options cant say!!
IMO E

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Re: S.D of consecutive nos.   [#permalink] 05 Sep 2008, 22:19
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# If two numbers are removed from 2, 4, 6, 8, 10, 12, 14, 16,

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