Bunuel wrote:
The table above shows the GPA of 20 students last semester. If the average (arithmetic mean) of the 20 GPAs is 2.95 and the standard deviation is 0.6, how many of the grades are more than 1.5 standard deviations away from the mean?
A. None
B. 1
C. 2
D. 3
E. 4
Attachment:
GradeTable.png
---------------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 0.61.5 standard deviations ABOVE the mean = 2.95 + 1.5(0.6) =
3.851.5 standard deviations BELOW the mean = 2.95 - 1.5(0.6) =
2.05How 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 3.85Check the values....
There are 4 such values.
Answer: E
Cheers,
Brent
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