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# List: 1, 3, 5, 7, 9, 11, 13, 15, 17, 19 If two numbers are

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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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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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Re: DS: Std Dev [#permalink]  08 Nov 2004, 06:05
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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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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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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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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Aspire

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