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Standard Deviation problem

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Standard Deviation problem

by sreak1089 » Sun Jul 19, 2009 10:27 am
This one is from GMATPrep exam:

The residents of Town X participated in a survey to determine the number hours per week each resident spent watching television. The distribution of the results of the survey had a mean of 21 hours and a standard deviation of 6 hours. The number of hours that Pat, a resident of Town X, watched television last week was between 1 and 2 standard deviations below the mean. Which of the following could be the number of hours that Pat watched televeision last week?

A) 30
B) 20
C) 18
D) 12
E) 6

OA D
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by Morgoth » Sun Jul 19, 2009 11:00 am
mean = 21

1 SD below from mean = 21 - 1*6 = 15

2 SD below from mean = 21 - 2*6 = 9


numbers of hours Pat watched television between 15 and 9

Hence D can be the only answer i.e 12.

Hope this helps.
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by sreak1089 » Sun Jul 19, 2009 8:00 pm
Thank you Morgoth.
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Re: Standard Deviation problem

by doclkk » Mon Jul 20, 2009 8:04 am
sreak1089 wrote:This one is from GMATPrep exam:

The residents of Town X participated in a survey to determine the number hours per week each resident spent watching television. The distribution of the results of the survey had a mean of 21 hours and a standard deviation of 6 hours. The number of hours that Pat, a resident of Town X, watched television last week was between 1 and 2 standard deviations below the mean. Which of the following could be the number of hours that Pat watched televeision last week?

A) 30
B) 20
C) 18
D) 12
E) 6

OA D
I think this boils down to an understanding of what standard deviation is.

Standard deviation is the average away from the average. So on this question, the standard deviation is given - but on questions where it will ask what's the standard deviation, find the mean, and kinda conceptualize what the average from the average is. I've found that standard deviation questions on the GMAT won't really test anything too "statistics" -

so if the question is about consecutive integers - you kinda have to gauge how many terms are in the set, what the avg is and think about what the standard deviation is.

In my experience, it's typically consecutive integers, the same numbers or number set like, "1,1,1,1,5,9,9,9,9" - where you can find the standard deviation very easily (4).

Your standard deviation knowledge typically have to be that deep so you should be fine.

Learn the quick things about standard deviations and you'll be fine.
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Re: Standard Deviation problem

by Ian Stewart » Mon Jul 20, 2009 9:41 am
doclkk wrote: In my experience, it's typically consecutive integers, the same numbers or number set like, "1,1,1,1,5,9,9,9,9" - where you can find the standard deviation very easily (4).
The standard deviation of the set {1,1,1,1,5,9,9,9,9} isn't equal to 4. You'll never need to do this on the GMAT, but to find standard deviation, we find all the distances to the average (here, eight of those distances are 4, and one is equal to 0), square them (so we now have eight values of 16 and one of 0), average these (so we get 8*16/9) and take the square root, which gives us 8*root(2)/3, which is a bit less than 4.

You may have been thinking of this set: {1,1,1,1,9,9,9,9}, which does indeed have a standard deviation of 4, because all of the distances to the average are equal to 4.
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