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For a certain distribution, the value 12.0 is one standard deviation

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Bunuel
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For a certain distribution, the value 12.0 is one standard deviation [#permalink] New post   22 Jul 2021, 06:15
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For a certain distribution, the value 12.0 is one standard deviation above the mean and the value 15.0 is three standard deviations above the mean. What is the mean of the data set?

A. 9.0
B. 9.5
C. 10.0
D. 10.5
E. 11.0
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Re: For a certain distribution, the value 12.0 is one standard deviation [#permalink] New post   22 Jul 2021, 06:35
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Between 12 and 15, we cover two standard deviations (we are going from 1 std deviation above the mean to 3 std deviations above the mean), so the standard deviation is 1.5, and if 12 is one standard deviation above the mean, the mean must be 12 - 1.5 = 10.5.
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Re: For a certain distribution, the value 12.0 is one standard deviation [#permalink] New post   22 Jul 2021, 12:22
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Bunuel wrote:
For a certain distribution, the value 12.0 is one standard deviation above the mean and the value 15.0 is three standard deviations above the mean. What is the mean of the data set?

A. 9.0
B. 9.5
C. 10.0
D. 10.5
E. 11.0


Let the mean be represented by M and the value be x
Given: M + x = 12(1)
Also, M + 3x = 15(2)
Subtracting (2) from (1):
2x = 3
x = 1.5
Putting the value of x in (1) or (2):
M = 10.5, IMO (D)!
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Re: For a certain distribution, the value 12.0 is one standard deviation [#permalink] New post   22 Jul 2021, 12:53
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m = mean & d = standard deviation

Given in question, value 12.0 is one standard deviation above the mean which means --> m + d = 12

Similarly, the value 15.0 is three standard deviations above the mean which means --> m + 3d = 15

Subtracting both equations --> m + 3d - m - d = 15 - 12 --> 2d = 3 --> d = 1.5

Substituting value of d in any equation, m + 1.5 = 12. hence, m = 10.5

Answer is Option D
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Re: For a certain distribution, the value 12.0 is one standard deviation [#permalink] New post   05 Nov 2023, 22:38
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Re: For a certain distribution, the value 12.0 is one standard deviation [#permalink]
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