Number question - SD and Mean type - The Beat The GMAT Forum - Expert GMAT Help & MBA Admissions Advice

Number question - SD and Mean type

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pradeepss: Junior | Next Rank: 30 Posts; Posts: 17; Joined: Wed May 30, 2007 10:51 am

by pradeepss » Sat Aug 17, 2013 3:56 pm

I do not understand what the question implys. i.e. what does it mean by a score of 58 was 2 SD below the mean AND score of 98 was 3 SD above the mean.

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Source: Beat The GMAT — Problem Solving | Sat Aug 17, 2013 3:56 pm

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Sat Aug 17, 2013 8:40 pm

For a certain examination, a score of 58 was 2 standard deviation below the mean and a score of 98 was 3 standard deviations above the mean. What was the mean score for the examination?
A 74
B 76
C 78
D 80
E 82

Here's one approach:

First, a little background on units of standard deviation:
If the SD is 4, then 1 unit of SD = 4
Similarly, 2 units of SD = 8
And 1.5 units of SD = 6
If the mean is 10 and the SD is 4, then we say that 18 is 2 units of SD above the mean since 10 + 2(4) = 18
Similarly, we say that 6 is 1 unit of SD below the mean since 10 - 4 = 6

For your question, we can let M=mean and let D=the standard deviation
So, 58 is 2 standard deviations below the mean translates into M - 2D = 58
and 98 is 3 standard deviations above the mean translates into M + 3D = 98

When we solve this system of equations, we get M=74 and D=8

So the answer is A

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Sat Aug 17, 2013 8:45 pm

For a certain examination, a score of 58 was 2 standard deviations below the mean and a score of 98 was 3 standard deviations above the mean. What was the mean score for the examination?
A 74
B 76
C 78
D 80
E 82

Here's another approach.

We can conclude that 58 and 98 are five standard deviations apart.
So, one standard deviation = (98 - 58)/5 = 8.

We're told that a score of 58 was 2 standard deviations below the mean
So, the mean = 58 + (2)(8) = 74

Answer: A

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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pradeepss: Junior | Next Rank: 30 Posts; Posts: 17; Joined: Wed May 30, 2007 10:51 am

by pradeepss » Sat Aug 17, 2013 10:28 pm

Thanks for introducing me to this concept.

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[email protected]: Elite Legendary Member; Posts: 10392; Joined: Sun Jun 23, 2013 6:38 pmFollowed by: 511 members; Location: Palo Alto, CA; Thanked: 2867 times; GMAT Score:800

by [email protected] » Sun Aug 18, 2013 12:21 pm

Hi pradeepss,

Standard Deviation is subject that the GMAT barely tests. You will never have to use the Standard Deviation formula on the GMAT, but the exam will test your basic understanding of what SD is (it's essentially how "spread out" a group of numbers is). Most Test Takers see just 1 Standard Deviation question, so it's not a big point gainer/loser. The broader category of statistics will be tested though; this includes mean, medium, mode and range, so be sure that you're clear on the definition of these terms and how to do the necessary math to solve for them.

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Rich

Contact Rich at [email protected]

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tarik: Senior | Next Rank: 100 Posts; Posts: 45; Joined: Tue May 21, 2013 10:22 am

by tarik » Mon Aug 19, 2013 4:26 pm

Thanks Pradeepss for introducing this topic and thanks Brent for all the explanations.

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