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Standard Deviation Question

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Senior | Next Rank: 100 Posts
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by anwarma » Tue Jun 10, 2008 7:11 am
Exact Wording,

For a certain examination, a score of 58 was 2 Standard Deviation (SD) below the mean, and a score of 98 was 3 SD ABOVE the mean. What was the mean score for the examination?

(A) 74 <-- ANSWER
(B) 76
(C) 78
(D) 80
(E) 82

My question is understanding the questions, so what is the simple way to understand this question. A score 58 and them using the 2 SD BELOW the mean , how do i use this info. Can some good soul rescue me from this dilemma :cry:
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by durgesh79 » Tue Jun 10, 2008 7:32 am
dont get too confused with complex words like "standard deviation"

This is actually a simple problem of algebra, presented to look like a complex statistical question.

We have two equations and two variables.

58 = M - 2*SD
98 = M + 3*SD

just solve these and you'll get M = 74.
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by VP_Jim » Tue Jun 10, 2008 8:38 am
Here's another way of thinking about it:

On this exam, 58 and 98 were five standard deviations apart. So, one standard deviation must be 8 (since 58 and 98 are 40 apart, and 40/5 = 8 ).

Thus, the mean must be 74, since 58 is two SDs below the mean (or 58+8+8 ). Just to verify, 98-8-8-8 (three SDs) also equals 74.

As already pointed out, this is a really easy question disguised as a difficult one!
Jim S. | GMAT Instructor | Veritas Prep
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