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# The residents of Town X participated in a survey to

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The residents of Town X participated in a survey to [#permalink]

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27 Mar 2008, 11:04
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The residents of Town X participated in a survey to determine the number of hours per week each resident spent watching television. The distribution of the results of the survey had a mean of 12 hours and a standard deviation of 6 hours. The number of hours that Pat, a resident of town X, matched 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 television last week?
(A) 30
(B) 20
(C) 18
(D) 12
(E) 6
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27 Mar 2008, 11:13
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First of all you should know what the standard deviation is. Standard deviation is deviation from the average/mean.
Say if mean is 10 and standard deviation is 5. Then all the number in that set should be within 10+5 or 10-5. Basically range is 5 - 15.

In question mean is given as 12, and standard deviation is 6.
So range is 12+6 and 12-6 (6 - 18).

If we check values 2 standard deviation away that mean 2*SD away.
So range will be 12+2*6 and 12-2*6 (0 - 24)

Question says Pat watched TV between 1 and 2 SD values.

So it can either be between 0 - 6 or 18 - 24.

Only answer which falls into this range is 20.

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27 Mar 2008, 11:23
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20 it is..

12+6+6=24

the result is between 18 and 24..

20 is the most likely..

this is probably a 400-500 level question..
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27 Mar 2008, 11:23
Thank you. Very well explained.
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27 Mar 2008, 12:12
why can't it be 6? E? I would think if it is between 1 to 2 sd then it would be 0-6. 6 is an answer choice and is below the mean, as it states. Therefore it can't be above 12. Am I right here?
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27 Mar 2008, 13:01
jingy77 wrote:
why can't it be 6? E? I would think if it is between 1 to 2 sd then it would be 0-6. 6 is an answer choice and is below the mean, as it states. Therefore it can't be above 12. Am I right here?

I agree with jingy77. If it's 1 to 2 s.d. below the mean. The answer should be E.
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27 Mar 2008, 13:03
jingy77 wrote:
why can't it be 6? E? I would think if it is between 1 to 2 sd then it would be 0-6. 6 is an answer choice and is below the mean, as it states. Therefore it can't be above 12. Am I right here?

It can be between 0 and 6 (excluding 0 and 6), and there is no such value in the answers. Picking 6 will mean it is within 1 SD and not between 1-2 SD.
Similarly it can be between 18 and 24 (excluding 18 and 24), and 20 is indeed one value within this range. Note that we did not pick up 18 as picking that mean it is within 1 SD and not between 1-2 SD.
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27 Mar 2008, 15:25
yeah, but it says 1-2 sd BELOW the mean.
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27 Mar 2008, 21:21
yea wouldn't this be E?

I'm confused.
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28 Mar 2008, 01:28
you say the range is from 0-6 and 18-24. But why can't the hrs be 6?
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28 Mar 2008, 06:51
Can we have the OA please? What is the source? If answer is indeed 20 then shoot an email to the source and ask them to make the wording clear.

Yes I agree that wording is little tricky here. Question in saying "between 1 and 2 standard deviations below the mean". However please note that "between 1 and 2 standard deviations" will be values 1, 2, 3, 4, and 5. 6 is not a value, which is "between 1 and 2 standard deviations", 6 is just 1 SD away from the mean so it cannot be the answer.

Now since 6 is out, we are left with other values. Another possible values "between 1 and 2 standard deviations" are 19, 20, 21, 22, and 23. Obviously we have 20 in the answers.
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02 Dec 2008, 14:07
In the GMATprep I met same task, only mean was 21, (not 12 as here) and correct answer for 21's mean is 12
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02 Dec 2008, 23:12
shils01 wrote:
The residents of Town X participated in a survey to determine the number of hours per week each resident spent watching television. The distribution of the results of the survey had a mean of 12 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 television last week?

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

It should be 6. Since the question says that Pat watched television between 1 and 2 SD below the mean, it rules out all choices above 6. Though the question is not properly worded, it should be 6.

When the question says below the mean, we cannot go above the mean.
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03 Dec 2008, 06:41
shils01 wrote:
The residents of Town X participated in a survey to determine the number of hours per week each resident spent watching television. The distribution of the results of the survey had a mean of 12 hours and a standard deviation of 6 hours. The number of hours that Pat, a resident of town X, matched 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 television last week?
(A) 30
(B) 20
(C) 18
(D) 12
(E) 6

Question clearly says The number of hours that Pat watched television last week was between 1 and 2 standard deviations below the mean hence answer should be 6 (E)
Re: PS Standard Deviation   [#permalink] 03 Dec 2008, 06:41
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