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Standard Deviation PS Question
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GMATGuruNY
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58<---d---><---d--->mean<---d---><---d---><---d--->98For 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 is the mean score for the examination.
1) 74
2) 76
3) 78
4) 80
5)82
As the figure above shows, there are a total of 5 standard deviations between 58 and 98.
Thus, d = (98-58)/5 = 8.
Since 58 is 2 standard deviations BELOW the mean, the mean = 58+d+d = 58+8+8 = 74.
The correct answer is A.
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Aside: A few words about units of standard deviation (via some examples)For a certain examination, a score of 58 was 2 standard deviatiation below the mean and a score of 98 was 3 S.D above the mean. What was the mean score for for the exam?
A. 74
B. 76
C. 78
D. 80
E. 82
If the mean of a population is 10, and the standard deviation is 2, then:
12 is one unit of standard deviation above the mean
14 is two units of standard deviation above the mean
16 is three units of standard deviation above the mean etc.
Conversely, 8 is one unit of standard deviation below the mean
6 is two units of standard deviation below the mean, and so on.
For this question, let M=mean and let D=standard deviation. We get two equations:
(1) M - 2D = 58
(2) M + 3D = 98
We can solve this system of equations for M to get M=74=A
ASIDE: We have two free videos on standard deviation:
- https://www.gmatprepnow.com/module/gmat- ... /video/806
- https://www.gmatprepnow.com/module/gmat- ... /video/809
Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
