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A certain list has an average of 6 and a standard deviation [#permalink]
18 Jul 2010, 12:33

00:00

A

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E

Difficulty:

25% (low)

Question Stats:

71% (01:44) correct
28% (00:43) wrong based on 76 sessions

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?

Re: Standard Deviation [#permalink]
18 Jul 2010, 13:09

5

This post received KUDOS

Expert's post

Raffy wrote:

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)

OA Later

"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.

Re: Standard Deviation [#permalink]
28 Jul 2010, 01:23

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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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

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

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.

Re: A certain list has an average of 6 and a standard deviation [#permalink]
11 Jul 2012, 09:49

+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.
_________________

"Life’s battle doesn’t always go to stronger or faster men; but sooner or later the man who wins is the one who thinks he can."

Re: A certain list has an average of 6 and a standard deviation [#permalink]
23 Jun 2013, 22:35

Expert's post

fozzzy wrote:

Tricky question! Is there an alternative solution?

This is a conceptual question. There is no so-called process that you can follow. You need to understand how SD is related to the average and the number of terms (through the SD formula). Once you do, you solve it by just looking at the options. Check out the links given above.
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