Standard Deviation

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kshin78: Senior | Next Rank: 100 Posts; Posts: 42; Joined: Tue Jun 17, 2008 1:18 pm; Thanked: 2 times

by kshin78 » Sat Aug 02, 2008 2:10 pm

Please help solve this problem.

The residents of Town X spends on avg 21 hours watching television with Standard deviation of 6 hours.

# of hrs Pat watched last week was between 1 and 2 standard deviation below the mean. Which of the following could be the # of hours pat wached last week?

a. 25
b. 20
c. 18
d. 12
e. 10

Thanks in advance.

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Source: Beat The GMAT — Problem Solving | Sat Aug 02, 2008 2:10 pm

msroopa: Newbie | Next Rank: 10 Posts; Posts: 2; Joined: Sat Aug 02, 2008 5:34 pm

by msroopa » Sat Aug 02, 2008 6:01 pm

1st SD is 15, 2nd SD is 9.
Hence number should be between 9 and 15.
Hence answer choice is D i.e 12

Let me know what is the correct answer.

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msroopa: Newbie | Next Rank: 10 Posts; Posts: 2; Joined: Sat Aug 02, 2008 5:34 pm

by msroopa » Sat Aug 02, 2008 6:05 pm

1st SD is 15, 2nd SD is 9.
Hence number should be between 9 and 15.
Hence answer choice is D i.e 12

Let me know what is the correct answer.

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kshin78: Senior | Next Rank: 100 Posts; Posts: 42; Joined: Tue Jun 17, 2008 1:18 pm; Thanked: 2 times

by kshin78 » Sat Aug 02, 2008 8:06 pm

You're right. It's d. 12.

It looks like you multiplied the std 6 to 1 & 2 and subtracted from 21 to get the range. Can you please explain why you did that?

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Stuart@KaplanGMAT: GMAT Instructor; Posts: 3225; Joined: Tue Jan 08, 2008 2:40 pmFollowed by: 614 members; Location: Toronto; Thanked: 1710 times; GMAT Score:800

by Stuart@KaplanGMAT » Sat Aug 02, 2008 11:40 pm

kshin78 wrote:You're right. It's d. 12.

It looks like you multiplied the std 6 to 1 & 2 and subtracted from 21 to get the range. Can you please explain why you did that?

The question is a LOT simpler than it sounds. You're really being tested on your understanding of the definition of "standard deviation".

Standard deviation measures how numbers are spread out (relative to the mean) in a set. A high standard deviation means that numbers are very spread out; a low standard deviation means that numbers are packed tightly together around the mean.

In this question, the standard deviation is 6 and the mean is 21.

So, 1 standard deviation is 21 +/- 6 (in other words, anyone who watches between 15 and 27 hours of TV is within 1 standard deviation of the mean).

2 standard deviations is 21 +/- (2*6), or 21 +/- 12 (in other words, anyone who watches between 9 and 33 hours of TV is within 2 standard deviations of the mean).

We know that Pat is between 1 and 2 SDs below the mean. Therefore, Pat watches somewhere between:

21-12 and 21-6 = 9 and 15 hours of TV a week.

Stuart Kovinsky | Kaplan GMAT Faculty | Toronto

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Hunsi: Junior | Next Rank: 30 Posts; Posts: 13; Joined: Sat Jul 05, 2008 8:20 am; Location: Muscat

by Hunsi » Sun Aug 03, 2008 5:26 am

Stuart Why cant the answer be 10? CHoice E

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kshin78: Senior | Next Rank: 100 Posts; Posts: 42; Joined: Tue Jun 17, 2008 1:18 pm; Thanked: 2 times

by kshin78 » Sun Aug 03, 2008 12:58 pm

thanks stuart!

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Stuart@KaplanGMAT: GMAT Instructor; Posts: 3225; Joined: Tue Jan 08, 2008 2:40 pmFollowed by: 614 members; Location: Toronto; Thanked: 1710 times; GMAT Score:800

by Stuart@KaplanGMAT » Sun Aug 03, 2008 1:04 pm

Hunsi wrote:Stuart Why cant the answer be 10? CHoice E

Actually, I didn't even look at the choices - 10 is also a valid answer.

Where is this question from?

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kshin78: Senior | Next Rank: 100 Posts; Posts: 42; Joined: Tue Jun 17, 2008 1:18 pm; Thanked: 2 times

by kshin78 » Sun Aug 03, 2008 1:36 pm

the question is from GMAT Prep. That's odd that it would have two valid answers....

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Stuart@KaplanGMAT: GMAT Instructor; Posts: 3225; Joined: Tue Jan 08, 2008 2:40 pmFollowed by: 614 members; Location: Toronto; Thanked: 1710 times; GMAT Score:800

by Stuart@KaplanGMAT » Sun Aug 03, 2008 7:48 pm

kshin78 wrote:the question is from GMAT Prep. That's odd that it would have two valid answers....

Yah.. so either the question is wrong, I messed up somewhere or you mistyped the answer choices... hmmm....

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gabriel: Legendary Member; Posts: 986; Joined: Wed Dec 20, 2006 11:07 amFollowed by: 1 member; Location: India; Thanked: 51 times

by gabriel » Mon Aug 04, 2008 5:42 am

moved to the PS section

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