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
Standard Deviation Question
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- Master | Next Rank: 500 Posts
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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.
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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- GMAT Instructor
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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!
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