Mean and standard Deviation

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marouan: Senior | Next Rank: 100 Posts; Posts: 38; Joined: Mon Oct 06, 2008 5:21 am

Mean and standard Deviation

by marouan » Fri Feb 06, 2009 8:43 am

If a certain sample of data has a mean of 20.0 and a standard deviation of 3.0, which of the following values is more than 2.5 standard deviation from the mean ?

* 12.0 ( right Answer )
* 13.5
* 17.0
* 23.5
* 26.5

Thanks.

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Source: Beat The GMAT — Problem Solving | Fri Feb 06, 2009 8:43 am

penumbra547: Junior | Next Rank: 30 Posts; Posts: 17; Joined: Tue Aug 05, 2008 4:15 pm

by penumbra547 » Fri Feb 06, 2009 9:29 am

I assume you are asking why the answer is (a).

if so, here is why.

Think of standard deviation(sd) as distance from the mean. So in this case, 2.5 times the sd is 2.5x3=7.5. <=== that's the distance from the mean.

therefore, you add and subtract 7.5 to the mean in order to get both extremes. in this case, it is 20+7.5=27.5, and 20-7.5=12.5. so imagine this range, from 27.5 and 12.5, and see which of the given values fall outside the range.

Voila! (A) is the answer.