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the table above
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21 Sep 2021, 01:17
21 Sep 2021, 01:17
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33% (01:30) correct
66% (01:22) wrong based on 18 sessions
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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
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Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
Re: the table above
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21 Sep 2021, 06:11
21 Sep 2021, 06:11
Carcass 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
---------------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
Re: the table above
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04 Dec 2022, 04:05
04 Dec 2022, 04:05
Hello from the GRE Prep Club BumpBot!
Thanks to another GRE Prep 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).
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Thanks to another GRE Prep 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.
