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Standard Deviation Problem - What is the Mean?

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by Bens4vcobra » Thu Jun 16, 2011 5:52 am
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

The answer is A but I don't know how to get there.
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by Brent@GMATPrepNow » Thu Jun 16, 2011 6:02 am
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
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
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by Bens4vcobra » Thu Jun 16, 2011 7:30 am
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
Fantastic! The light came on after reading your method.
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by sanju09 » Wed Aug 29, 2012 12:51 pm
Brent@GMATPrepNow wrote:
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
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
nice
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