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Problem with Standard Deviation

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Problem with Standard Deviation

by pseudonym » Mon Aug 30, 2010 9:14 am
A certain list of 100 data has an arithmetic mean of 6 and standard deviation d, where d is positive. Which of the following pairs of data, when added to the list, must results 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

The answer is E. Can someone pls explain why?

Thx, H
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by Gurpinder » Mon Aug 30, 2010 9:20 am
pseudonym wrote:A certain list of 100 data has an arithmetic mean of 6 and standard deviation d, where d is positive. Which of the following pairs of data, when added to the list, must results 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

The answer is E. Can someone pls explain why?

Thx, H
Hey,

The key to understanding this question is knowing what Standard Deviation (SD) is. In simple language, SD = how much does X vary from the AVERAGE of the set that X belongs to. if the Avg of a Set = 3 and X = 5. X = 2 SD away from the mean. Alright now the question.

100 data has a mean of 6 and sd = d

The trick is, the close your data is to the mean, the lower your SD will go. Why? Because SD = how much does X vary from the AVERAGE.

Therefore, E) 6 and 6 will lower the SD because both values are exactly equal to the average.

Does this clarify?
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by pseudonym » Mon Aug 30, 2010 9:39 am
Yeah i figured that out too, the bit that confused me was why C is not possible...the question is must reduce the std dev, not which pair reduces it the most? C reduces the std dev, rite?
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by Gurpinder » Mon Aug 30, 2010 9:41 am
pseudonym wrote:Yeah i figured that out too, the bit that confused me was why C is not possible...the question is must reduce the std dev, not which pair reduces it the most? C reduces the std dev, rite?
No, It would increase the value of SD.

C) 0 and 6

The 6 is exactly at the mean. But the 0 is 6 away from the mean, so SD will increase.
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by beatthegmatinsept » Mon Aug 30, 2010 9:47 am
This is a nice trick question. If you know the mean/SD concept well, you can answer this question in less than 30 seconds. If you don't then you can plus in values using a smaller set of data and try calculating the mean and sd.
Whats the source of this question?
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by pseudonym » Mon Aug 30, 2010 9:51 am
GMAT Prep 2 (2nd test on the downloaded software).
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by beatthegmatinsept » Mon Aug 30, 2010 9:54 am
pseudonym wrote:GMAT Prep 2 (2nd test on the downloaded software).
Sad.. I am saving GMAT Prep test for the last 2 weeks before my exam, and I just saw one of the questions :(
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by pseudonym » Mon Aug 30, 2010 9:57 am
Not a problem dude, I repeated GMAT prep 1 after 2 wks, only 3-4 of the ques got repeated. In fact I spent too much time on the tough ones that got repeated and got 2 of them wrong. As long as you don't have the answer memorized.

I plan on retaking GMAT Prep 2 after 2 days. Test is this weekend. :)
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by beatthegmatinsept » Mon Aug 30, 2010 9:59 am
pseudonym wrote:Not a problem dude, I repeated GMAT prep 1 after 2 wks, only 3-4 of the ques got repeated. In fact I spent too much time on the tough ones that got repeated and got 2 of them wrong. As long as you don't have the answer memorized.

I plan on retaking GMAT Prep 2 after 2 days. Test is this weekend. :)
Really? That's good to hear :) Thanks!
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by Stuart@KaplanGMAT » Mon Aug 30, 2010 10:16 am
Gurpinder wrote:
pseudonym wrote:Yeah i figured that out too, the bit that confused me was why C is not possible...the question is must reduce the std dev, not which pair reduces it the most? C reduces the std dev, rite?
No, It would increase the value of SD.

C) 0 and 6

The 6 is exactly at the mean. But the 0 is 6 away from the mean, so SD will increase.
Small correction:

the question asks for the pair which MUST reduce the standard deviation of the set. Since we know that the set currently has a positive standard deviation, the only way to GUARANTEE that our pair reduces SD is to choose data points directly on the mean.

All of the other choices MIGHT reduce the SD of the set - it depends on the current value of d. For example, if the current value of d is 200, then every answer choice would lead to a reduction in SD. However, if the current value of d is .01, then only (E) would lead to a reduction.
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by missrochelle » Mon Aug 30, 2010 10:52 am
that makes a lot of sense -- so by choosing points directly on the mean. you dont change the numerator, but the denominator goes up...

this correction really helped clear it up....
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by uwhusky » Mon Aug 30, 2010 10:56 am
exactly, missrochelle!
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