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A set has an average (arithmetic mean) of 42 and a standard deviation
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21 Sep 2021, 01:15
21 Sep 2021, 01:15
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Question Stats:
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A set has an average (arithmetic mean) of 42 and a standard deviation of 1.8. Which of the following values is two standard deviations away from the mean?
A. 36
B. 38.4
C. 40.2
D. 43.8
E. 75.6
A. 36
B. 38.4
C. 40.2
D. 43.8
E. 75.6
Retired Moderator
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Re: A set has an average (arithmetic mean) of 42 and a standard deviation
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21 Sep 2021, 06:10
21 Sep 2021, 06:10
Carcass wrote:
A set has an average (arithmetic mean) of 42 and a standard deviation of 1.8. Which of the following values is two standard deviations away from the mean?
A. 36
B. 38.4
C. 40.2
D. 43.8
E. 75.6
A. 36
B. 38.4
C. 40.2
D. 43.8
E. 75.6
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.
-----------------------------
For this question, if the standard deviation is 1.8, then two standard deviations = (2)(1.8) = 3.6
So, two standard deviations BELOW the mean = 42 - 3.6 = 38.4
And two standard deviations ABOVE the mean = 42 + 3.6 = 45.6
This means there are two correct answers.
Now check the answer choices for one of the two possible answers.
Answer: B
gmatclubot
Re: A set has an average (arithmetic mean) of 42 and a standard deviation [#permalink]
21 Sep 2021, 06:10
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