---------------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.
----ONTO THE QUESTION!!!------------------------

The average (arithmetic mean) of the 20 GPAs is 2.95 and the standard deviation is 0.6
1.5 standard deviations ABOVE the mean = 2.95 + 1.5(0.6) = 3.85
1.5 standard deviations BELOW the mean = 2.95 - 1.5(0.6) = 2.05

How many of the grades are MORE THAN 1.5 standard deviations away from the mean?
So, we're looking for grades that are EITHER less than 2.05 OR greater than 3.85

Check the values....


There are 4 such values.

Answer: E

Cheers,
Brent
_________________

Since the mean is 2.95 and we need to find which of the GPA's lies within 1.5 SD's
we need to establish the range.
This range is 2.95 - 0.9 = 2.05 and 2.95 + 0.9 = 3.85

The 4 values which lie outside this range are 1.9,1.8,3.9 and 4.0(Option E)
_________________

1.5 SD = 1.5 * 0.6 = 0.9

The range will be
2.95 - 0.9 = 2.05 and 2.95 + 0.9 = 3.85

4 values,,option E

This problem tests your understanding of how the standard deviation is used within a set of data. Because the standard deviation is 0.6, then 1.5 standard deviations will be a distance of (1.5)(0.6), or 0.9. And since standard deviation measures how far data is from the mean, your job is to determine which data points fall farther than 0.9 away from the mean of 2.95. That means that on the low end you're looking for values below:

And on the high end you're looking for values above:

On the high side, only 3.9 and 4.0 are greater than 3.85, and on the low side only 1.9 and 1.8 are less than 2.05.

Therefore there are four such values that fit the criteria, so the correct answer is E.

1.5 standard deviations is 1.5 x 0.6 = 0.9.

So 1.5 standard deviations above the mean is 2.95 + 0.9 = 3.85, and 1.5 standard deviations below the mean is 2.95 - 0.9 = 2.05.

Looking at the chart, we see that 4 grades (1.8, 4.0, 1.9 and 3.9) are more than 1.5 standard deviations away from the mean.

Answer: E
_________________

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________