Mean and Standard Deviation

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nakul_anand: Senior | Next Rank: 100 Posts; Posts: 74; Joined: Fri Oct 09, 2009 4:20 pm; Thanked: 4 times

Mean and Standard Deviation

by nakul_anand » Sun May 09, 2010 7:45 am

The class mean score on a test was 60, and the standard deviation was 15. If Jack's score was within 2 standard deviations of the mean, what is the lowest score he could have received?

(A) 30
(B) 31
(C) 45
(D) 90
(E) 89

[spoiler]OA:A[/spoiler]

I am not sure that I understand the meaning of 'within 2 standard deviations'...

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Source: Beat The GMAT — Problem Solving | Sun May 09, 2010 7:45 am

Ashish8: Senior | Next Rank: 100 Posts; Posts: 52; Joined: Sat Jan 23, 2010 9:08 pm; Thanked: 2 times

by Ashish8 » Sun May 09, 2010 7:49 am

The lowest and highest scores within one standard deviation is 45 and 75, respectively.

Two standard deviations would be 15 * 2, hence the lowest and highest would be 30 and 90.

Answer A.

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nakul_anand: Senior | Next Rank: 100 Posts; Posts: 74; Joined: Fri Oct 09, 2009 4:20 pm; Thanked: 4 times

by nakul_anand » Sun May 09, 2010 8:38 am

Okay...This is where I get confused...

Within 2 Standard Deviations - doesn't that mean within the limits of the 2 SDs?

limits are 30 and 90....so wouldn't 'within 2 SDs' mean that 31 will be the lowest score?

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Ashish8: Senior | Next Rank: 100 Posts; Posts: 52; Joined: Sat Jan 23, 2010 9:08 pm; Thanked: 2 times

by Ashish8 » Sun May 09, 2010 8:58 am

Standard deviation is distance from average.

so 30 is the max away from average on the low end.

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

by Stuart@KaplanGMAT » Sun May 09, 2010 12:47 pm

nakul_anand wrote:Okay...This is where I get confused...

Within 2 Standard Deviations - doesn't that mean within the limits of the 2 SDs?

limits are 30 and 90....so wouldn't 'within 2 SDs' mean that 31 will be the lowest score?

Hi,

if 15 is one SD, then 30 is two SDs. "Within" includes the maximum limit of the range.

For example, if the northernmost street in your city is called "GMAT Avenue" and you live on GMAT Avenue, it would still be correct for you to say that you live within the city.

Here's another way you can arrive at 30: nowhere does it say in the question that scores have to be integers. So, if 30 wasn't included within 2 standard deviations, then 30.1, 30.2, 30.3, etc... would all be possible scores lower than 31 that are clearly within 2 SDs. Since 31 can't be the correct answer, 30 must be.