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The table above shows the GPA of 20 students last semester. If the ave

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The table above shows the GPA of 20 students last semester. If the ave  [#permalink]

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New post 06 Jun 2017, 09:55
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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
GradeTable.png [ 2.32 KiB | Viewed 1664 times ]

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Re: The table above shows the GPA of 20 students last semester. If the ave  [#permalink]

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New post 06 Jun 2017, 10:34
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)
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Re: The table above shows the GPA of 20 students last semester. If the ave  [#permalink]

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New post 07 Jun 2017, 11:25
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
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The table above shows the GPA of 20 students last semester. If the ave  [#permalink]

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New post 25 Sep 2018, 23:27
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:
Quote:
2.95 - 0.9 = 2.05


And on the high end you're looking for values above:
Quote:
2.95 + 0.9 = 3.85.


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.

Quote:
Most common mistake that happens in this question, when the test taker forgets to account for the 1.5 standard deviation i.e.to determine which data points fall farther than 0.9 away from the mean of 2.95

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Re: The table above shows the GPA of 20 students last semester. If the ave  [#permalink]

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New post 28 Jan 2019, 09:46
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Bunuel wrote:
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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



---------------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....
Image

There are 4 such values.

Answer: E

Cheers,
Brent

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Re: The table above shows the GPA of 20 students last semester. If the ave  [#permalink]

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New post 30 Jan 2019, 19:15
Bunuel wrote:
Image
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


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
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Re: The table above shows the GPA of 20 students last semester. If the ave   [#permalink] 30 Jan 2019, 19:15
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