Problem Solving

adi wrote: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

If we let x = mean and s = standard deviation, then a score of 58 that was 2 standard deviations below the mean would mean 58 = x - 2s. Similarly, a score of 98 that was 3 standard deviations above the mean would mean 98 = x + 3s.

We can use the two equations to determine a value of x.

x - 2s = 58

x + 3s = 98

If we subtract the first equation from the second equation, we have:

5s = 40

s = 8

Now we can determine x:

x + 3s = 98

x + 3(8) = 98

x + 24 = 98

x = 74

Answer: A

Hi All,

We're told that 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. We're asked for the mean score for the examination. The math behind this question is just basic Algebra, but depending on how you organize your information, you can save some time on the math that you'll need to do.

To start, the difference between a 98 and a 58 is 5 total Standard Deviations (since a 98 is '3 above' and a 58 is '2 below'). Thus, 98 - 58 = 40 is equal to 5 Standard Deviations.
40/5 = 8... meaning that 1 Standard Deviation is 8 'away' from the mean. At this point, we can either "go up" from 58 or "go down" from 98, but we'll get to the Mean either way as long as we're counting up the proper number of Standard Deviations.

From 58, we add 2 S.D.s --> 58 + 2(8) = 74
From 98, we subtract 3 S.D.s --> 98 - 3(8) = 74

Final Answer: A

GMAT assassins aren't born, they're made,
Rich