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I'm sure there's an easy solution to this one, but I haven't

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I'm sure there's an easy solution to this one, but I haven't [#permalink] New post 14 Sep 2006, 10:05
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I'm sure there's an easy solution to this one, but I haven't figured it out yet.

A certain list of 100 data has a mean of 6 and a 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 standard deviation less than D?

A. -6 and 0
B. 0 and 0
C. 0 and 6
D. 0 and 12
E. 6 and 6

Last edited by eazyb81 on 16 Sep 2006, 08:04, edited 1 time in total.
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Re: PS - Standard Deviation [#permalink] New post 14 Sep 2006, 10:41
eazyb81 wrote:
I'm sure there's an easy solution to this one, but I haven't figured it out yet.

A certain list of 100 data has a mean of 6 and a 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 standard deviation less than D?

A. -6 and 0
B. 0 and 0
C. 0 and 6
D. 0 and 12
E. 6 and -6



--------------------- deviations sum to
A. -6 and 0 ------------------- 18 SD is greater than D
B. 0 and 0 ------------------- 12
C. 0 and 6 ------------------- 6 Correct Answer
D. 0 and 12 ------------------- 12
E. 6 and -6 ------------------- 12
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 [#permalink] New post 14 Sep 2006, 12:10
Any other thoughts?

This was the first question I had in a recent practice test, and I was (and still am) really confused by it.

C is not the correct answer....
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Re: PS - Standard Deviation [#permalink] New post 14 Sep 2006, 12:29
kevincan wrote:
eazyb81 wrote:
I'm sure there's an easy solution to this one, but I haven't figured it out yet.

A certain list of 100 data has a mean of 6 and a 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 standard deviation less than D?

A. -6 and 0
B. 0 and 0
C. 0 and 6
D. 0 and 12
E. 6 and -6


Are you sure it's well written?


I copied it directly from GMATPrep this morning.
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 [#permalink] New post 14 Sep 2006, 12:50
I've seen this problem before, I believe the answer E should read 6 and 6 not 6 and -6 (or at least one of the answer choices should read 6 and 6). By adding two additional 6s, the std dev will be reduced and that data points will be 102.
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 [#permalink] New post 14 Sep 2006, 13:07
Cedars wrote:
I've seen this problem before, I believe the answer E should read 6 and 6 not 6 and -6 (or at least one of the answer choices should read 6 and 6). By adding two additional 6s, the std dev will be reduced and that data points will be 102.


My mistake, you are right, E should read 6 and 6......sorry guys.

Do the data points go up to 102 just because we are adding two additional numbers? If so, doesn't every listed choice make the data points go up to 102?

Why does the S.D. reduce only when you add 6 and -6? This is going over my head.
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 [#permalink] New post 14 Sep 2006, 20:04
eazyb81 wrote:
My mistake, you are right, E should read 6 and 6......sorry guys.

Do the data points go up to 102 just because we are adding two additional numbers? If so, doesn't every listed choice make the data points go up to 102?

Why does the S.D. reduce only when you add 6 and -6? This is going over my head.

By adding two more sixes, you're increasing the number of data points closer to the mean. Since SD measures spread, this decreases the SD.

But, I have a question of my own. Going by the explanation I have in my mind, adding -6 and 0 should bring increase the SD in the negative direction, right, or am I totally lost? :? [/code]
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 [#permalink] New post 15 Sep 2006, 06:44
anandsebastin wrote:
eazyb81 wrote:
My mistake, you are right, E should read 6 and 6......sorry guys.

Do the data points go up to 102 just because we are adding two additional numbers? If so, doesn't every listed choice make the data points go up to 102?

Why does the S.D. reduce only when you add 6 and -6? This is going over my head.

By adding two more sixes, you're increasing the number of data points closer to the mean. Since SD measures spread, this decreases the SD.

But, I have a question of my own. Going by the explanation I have in my mind, adding -6 and 0 should bring increase the SD in the negative direction, right, or am I totally lost? :? [/code]


Same problem I am having.....any Quant masters care to explain this?

This was my first question in a recent practice test so I assume that there is an easy explanation, but i'm just not seeing it.
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 [#permalink] New post 15 Sep 2006, 10:31
Thank god it was a typo :) I get all worked up when I can't figure out a GMATPrep question.

The best way to find out the answer to this problem is to find the sum of moments around the mean for each answer choice.

moment is calculated by summation of[(value-mean)^2]

A. -6 and 0: sum of moments = (-6-6)^2 + (0-6)^2 = 144+36=180
B. 0 and 0 : 36+36 = 72
C. 0 and 6 : 36+0 = 36
D. 0 and 12 : 36+36=72
E. 6 and 6: 0+0 = 0

Clearly E is the only one which certainly reduces the average of the sum of moments.
  [#permalink] 15 Sep 2006, 10:31
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