Problem Solving

For a certain examination, a score of 58 was 2 standard deviation 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

Here's one approach:

First, a little background on units of standard deviation:
If the SD is 4, then 1 unit of SD = 4
Similarly, 2 units of SD = 8
And 1.5 units of SD = 6
If the mean is 10 and the SD is 4, then we say that 18 is 2 units of SD above the mean since 10 + 2(4) = 18
Similarly, we say that 6 is 1 unit of SD below the mean since 10 - 4 = 6

For your 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

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

Here's another approach.

We can conclude that 58 and 98 are five standard deviations apart.
So, one standard deviation = (98 - 58)/5 = 8.

We're told that a score of 58 was 2 standard deviations below the mean
So, the mean = 58 + (2)(8) = 74

Answer: A

Cheers,
Brent

Hi pradeepss,

Standard Deviation is subject that the GMAT barely tests. You will never have to use the Standard Deviation formula on the GMAT, but the exam will test your basic understanding of what SD is (it's essentially how "spread out" a group of numbers is). Most Test Takers see just 1 Standard Deviation question, so it's not a big point gainer/loser. The broader category of statistics will be tested though; this includes mean, medium, mode and range, so be sure that you're clear on the definition of these terms and how to do the necessary math to solve for them.

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