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arithmetic mean and standard deviation

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patrickgong6688
 Post subject: arithmetic mean and standard deviation
 Post Posted: Fri Jul 08, 2011 11:51 am 
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The arithmetic mean of a data set is 46 and the standard deviation of the set is 4.Which value is exactly 1.5 standard deviation from the arithmetic mean of the set?
A42 B44.5 C47.5 D.50 E52
The answer is E
I do not know why.Can you give me a explaination?
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adrielfrederick
 Post subject: Re: arithmetic mean and standard deviation
 Post Posted: Mon Jul 11, 2011 1:29 pm 
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Students


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Standard deviation is a measure used to indicate the amount of deviation away from the mean.

If I say I am one standard deviation away from the mean I can be at Mean-SD or Mean +SD

In your case 1.5 SD works out to be 6 . Therefore Mean +SD works out to be 52
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jnelson0612
 Post subject: Re: arithmetic mean and standard deviation
 Post Posted: Thu Jul 14, 2011 12:27 pm 
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ManhattanGMAT Staff


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Yes, just take the standard deviation given (4) multiplied by the number of standard deviations the problem is interested in (1.5). In this case we get 6. Add and subtract that to the mean of 46; we get -1.5 standard deviations at 40 and +1.5 standard deviations at 52.

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Jamie Nelson
ManhattanGMAT Instructor
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patrickgong6688
 Post subject: Re: arithmetic mean and standard deviation
 Post Posted: Mon Aug 08, 2011 7:12 pm 
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Thank you So much! I understand!
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jnelson0612
 Post subject: Re: arithmetic mean and standard deviation
 Post Posted: Wed Aug 17, 2011 6:06 pm 
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Posts: 1857
Great!

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Jamie Nelson
ManhattanGMAT Instructor
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