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Intern
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List: 1, 3, 5, 7, 9, 11, 13, 15, 17, 19 If two numbers are [#permalink]
 08 Nov 2004, 03:00
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List: 1, 3, 5, 7, 9, 11, 13, 15, 17, 19
If two numbers are removed from the list, will there be a change in the standard deviation of the remaining 8 numbers?
1. the median of the eight numbers is 10
2. the mean of the eight numbers is the same as the original mean
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Manager
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I'd go for D
Question stem yields: mean = median =10.
Statement 1 means numbers removed are symmetric with respect to the median. Nevertheless, shape of distribution is altered hence std has to be different from that of the initial data.
Statement 2 leads to the same conclusions as statement 1.
Time =~30s
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Manager
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linker wrote: List: 1, 3, 5, 7, 9, 11, 13, 15, 17, 19
If two numbers are removed from the list, will there be a change in the standard deviation of the remaining 8 numbers?
1. the median of the eight numbers is 10
2. the mean of the eight numbers is the same as the original mean
I go for B
In (1) we can remove 1 and 13, or 7 and 19. The mean of the numbers will be the same, but the standard deviation will not.
In (2) two numbers are removed simmetrically (ie 1 and 19, or 5 and 13). This will not change the std dvt.
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GMAT Club Legend
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Oops, D it is as ST Dev will inadvertently change. A "no" answer is sufficient.
If we remove 1-19 or 3-17, this will change the st-dev. in either choice 1 or 2. Good st. dev. question. As a matter of fact, this question is self-sufficient in the sense that ANY two numbers you will remove will change the st.dev. 
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Paul
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Manager
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B is my choice.
1. take out 1 & 19, standard deviation is the same. But take 1 & 13, standar deviation changes even though median is still 10. So 1 out.
2. Sufficient
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Manager
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Ans is D. If 2 numbers are removed, the SD will change anyway.
The only case where the SD will remain the same is if the sum of the square of differences reduce by 1/5th of the original value. This condition will not be satisfied as it is a fraction. So, removing any number from the list will change the SD.
Does anyone know any simpler way of attacking the problem 
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Thanks !
Aspire
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