A certain list has an average of 6 and a standard deviation

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A certain list has an average of 6 and a standard deviation [#permalink]

18 Jul 2010, 13:33

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A certain list has an average of 6 and a standard deviation of d (d is positive). Which of the following pairs of data when added to the list, must result in a list of 102 data with standard deviation less than d?

A. (-6;0)
B. (0;0)
C. (0;6)
D. (0;12)
E. (6;6)

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Re: Standard Deviation [#permalink]

18 Jul 2010, 14:09

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Raffy wrote:

"Standard deviation shows how much variation there is from the mean. A low standard deviation indicates that the data points tend to be very close to the mean, whereas high standard deviation indicates that the data are spread out over a large range of values."

So when we add numbers, which are far from the mean we are stretching the set making SD bigger and when we add numbers which are close to the mean we are shrinking the set making SD smaller.

According to the above adding two numbers which are closest to the mean will shrink the set most, thus decreasing SD by the greatest amount.

Closest to the mean are 6 and 6 (actually these numbers equal to the mean) thus adding them will definitely shrink the set, thus decreasing SD.

Answer: E.

For more on this issue please check Standard Deviation chapter of Math Book (link in my signature) and the following two topics for practice:
ps-questions-about-standard-deviation-85897.html
ds-questions-about-standard-deviation-85896.html
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Re: Standard Deviation [#permalink]

18 Jul 2010, 23:39

thanks Bunuel, but is there any mathematical method also to calculate the same??

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Re: Standard Deviation [#permalink]

27 Jul 2010, 15:45

Bunuel, you are a genius. Amazing explanation.

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Re: Standard Deviation [#permalink]

28 Jul 2010, 02:23

Thank you Bunuel, I just add 1 following remark.
E is only correct if we take into account that d is positive. In case of d=0, the SD remains the same.
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GMAT PREP PS [#permalink]

24 Aug 2010, 18:29

How do answer choices C and E differ?

A certain list of 100 data has an average of 6 and standard deviation of d where d is positive. Which of the following pairs of data, when added to the list must result in a list of 102 data with the standard deviation less than d?
(A) 0 and 6
(B) 0 and 12
(C) 0 and 0
(D) -6 and 0
(E) 6 and 6

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Re: GMAT PREP PS [#permalink]

11 Jul 2012, 01:40

uzzy12 wrote:

Option E offers two numbers equal to the mean while other options (including C) offer number(s) different from the mean. Adding two numbers which are closest to the mean (option E in our case ) will shrink the set most, thus decreasing SD by the greatest amount.

Complete solution: a-certain-list-has-an-average-of-6-and-a-standard-deviation-97473.html#p751013
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Re: A certain list has an average of 6 and a standard deviation [#permalink]

11 Jul 2012, 10:49

+1 E

This is a conceptual question. If you add more data to the average, more data will be closer to the average. Hence, the standard deviation is lower.
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Re: A certain list has an average of 6 and a standard deviation [#permalink]

11 Jul 2012, 23:14

metallicafan wrote:

+1 E

This is a conceptual question. If you add more data to the average, more data will be closer to the average. Hence, the standard deviation is lower.

Yes, you are right. For a detailed discussion of this concept, check out these posts:

http://www.veritasprep.com/blog/2012/06 ... deviation/

http://www.veritasprep.com/blog/2012/06 ... n-part-ii/
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Re: A certain list has an average of 6 and a standard deviation [#permalink] 11 Jul 2012, 23:14

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A certain list has an average of 6 and a standard deviation

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