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If a certain sample of data has a mean of 20.0 and a standar
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14 Sep 2020, 10:23
14 Sep 2020, 10:23
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Question Stats:
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If a certain sample of data has a mean of 20.0 and a standard deviation of 3.0, which of the following values is more than 2.5 standard deviations from the mean?
A. 12.0
B. 13.5
C. 17.0
D. 23.5
E. 26.5
Source: GMAT
A. 12.0
B. 13.5
C. 17.0
D. 23.5
E. 26.5
Source: GMAT
Re: If a certain sample of data has a mean of 20.0 and a standar
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14 Sep 2020, 10:23
14 Sep 2020, 10:23
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Question From Our New Project: GRE Quant Challenge Questions Daily - NEW EDITION!
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For more theory and practice see our GRE - Math Book
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Re: If a certain sample of data has a mean of 20.0 and a standar
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14 Sep 2020, 10:37
14 Sep 2020, 10:37
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Carcass wrote:
If a certain sample of data has a mean of 20.0 and a standard deviation of 3.0, which of the following values is more than 2.5 standard deviations from the mean?
A. 12.0
B. 13.5
C. 17.0
D. 23.5
E. 26.5
Source: GMAT
A. 12.0
B. 13.5
C. 17.0
D. 23.5
E. 26.5
Source: GMAT
-------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.
-----------------------------
So, 2.5 standard deviations = (2.5)(3) = 7.5
20 - 7.5 = 12.5
So, 12.5 is 2.5 standard deviations BELOW the mean
20 + 7.5 = 27.5
So, 27.5 is 2.5 standard deviations ABOVE the mean
Answer choice A (12) is more than 2.5 standard deviations from the mean
Answer: A
