MaithiliGokarn wrote:
For a certain exam,a score of 58 was 2 standard deviations below mean and a score of 98 was 3 standard deviations above mean.What was the mean score for the exam?
A. 74
B. 76
C. 78
D. 80
E. 82
----------ASIDE---------------------
A little extra background on
standard deviations above and below the mean If, for example, a set has a standard deviation of 4, then:
1 standard deviation = 4
2 standard deviations = 8
3 standard deviations = 12
1.5 standard deviations = 6
0.25 standard deviations = 1
etc
So, if the mean of a set is 9, and the standard deviation is 4, then:
2 standard deviations ABOVE the mean =
17 [since 9 + 2(4) = 17] 1.5 standard deviations BELOW the mean =
3 [since 9 - 1.5(4) = 3] 3 standard deviations ABOVE the mean =
21 [since 9 + 3(4) = 21] etc.
-------------------------------------------------------------
For this 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
I’ve spent the last 20 years helping students overcome their difficulties with GMAT math, and the biggest thing I’ve learned is…
Many students fail to maximize their quant score NOT because they lack the skills to solve certain questions but because they don’t understand what the GMAT is truly testing -
Learn more