Problem Solving

AAPL wrote:GMAT Prep

If a certain sample of data has a mean of 20.0 and a standard deviation of 3.0, which of the following values is more than 2.5 standard deviations from the mean?

A. 12.0
B. 13.5
C. 17.0
D. 23.5
E. 26.5

OA A

2.5 standard deviations above the mean is 2.5 x 3 + 20 = 7.5 + 20 = 27.5.

2.5 standard deviations below the mean is 20 - 2.5 x 3 = 20 - 7.5 = 12.5.

Thus, a value more than 2.5 standard deviations from the mean would be one that is either greater than 27.5 or less than 12.5. So the correct answer is 12.

Answer: A

AAPL wrote:GMAT Prep

If a certain sample of data has a mean of 20.0 and a standard deviation of 3.0, which of the following values is more than 2.5 standard deviations from the mean?

A. 12.0
B. 13.5
C. 17.0
D. 23.5
E. 26.5

OA A

-------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.
-----------------------------
So, 2.5 standard deviations = (2.5)(3) = 7.5

20 - 7.5 = 12.5
So, 12.5 is 2.5 standard deviations BELOW the mean

20 + 7.5 = 27.5
So, 27.5 is 2.5 standard deviations ABOVE the mean

Answer choice A (12) is more than 2.5 standard deviations from the mean

Answer: A