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Typically, the GMAT uses the term "units of standard deviation"Bens4vcobra wrote:For a certain exam, 58 was 2 standard deviations below the mean, and 98 was 3 standard deviations above the mean. What is the mean?
A)74
B)76
C)78
D)80
E)82
Fantastic! The light came on after reading your method.Brent@GMATPrepNow wrote: Typically, the GMAT uses the term "units of standard deviation"
So, if the SD is 4, then 1 unit of SD = 4
Similarly, 2 units of SD = 8
And 1.5 units of SD = 6
If the mean is 10 and the SD is 4, then we say that 18 is 2 units of SD above the mean since 10 + 2(4) = 18
Similarly, we say that 6 is 1 unit of SD below the mean since 10 - 4 = 4
For your question, we can let M=mean and let D=the standard deviation
So, 58 is 2 standard deviations below the mean translates into M - 2D = 58
and 98 is 3 standard deviations above the mean translates into M + 3D = 98
When we solve this system of equations, we get M=74 and D=8
So the answer is A
niceBrent@GMATPrepNow wrote:Typically, the GMAT uses the term "units of standard deviation"Bens4vcobra wrote:For a certain exam, 58 was 2 standard deviations below the mean, and 98 was 3 standard deviations above the mean. What is the mean?
A)74
B)76
C)78
D)80
E)82
So, if the SD is 4, then 1 unit of SD = 4
Similarly, 2 units of SD = 8
And 1.5 units of SD = 6
If the mean is 10 and the SD is 4, then we say that 18 is 2 units of SD above the mean since 10 + 2(4) = 18
Similarly, we say that 6 is 1 unit of SD below the mean since 10 - 4 = 4
For your question, we can let M=mean and let D=the standard deviation
So, 58 is 2 standard deviations below the mean translates into M - 2D = 58
and 98 is 3 standard deviations above the mean translates into M + 3D = 98
When we solve this system of equations, we get M=74 and D=8
So the answer is A
