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06 Jun 2017, 09:55
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
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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 [ 2.32 KiB | Viewed 8702 times ]
Updated on: 22 Jan 2020, 17:20
Originally posted by BrentGMATPrepNow on 28 Jan 2019, 09:46.
Last edited by BrentGMATPrepNow on 22 Jan 2020, 17:20, edited 1 time in total.
Last edited by BrentGMATPrepNow on 22 Jan 2020, 17:20, edited 1 time in total.
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Bunuel
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 0.6
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
General Discussion
06 Jun 2017, 10:34
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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)
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)
