Math problem

[src_saurav]

If two deviations down the mean is 58 and three up is 98. What is the mean?

Please help

[Brent@GMATPrepNow]

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.
-----------------------------

Okay, now onto your question:

If two deviations down the mean is 58 and three up is 98. What is the mean?

Let M = the mean
Let d = 1 standard deviation

two [standard] deviations down [below] the mean is 58
So, M - 2d = 58

three deviations above the mean is 98
So, M + 3d = 98

We now have the following system that we can solve for M:
M - 2d = 58
M + 3d = 98

Subtract the top equation from the bottom equation to get: 5d = 40
Solve to get d = 8

Now that we know d = 8, plug d = 8 into one of the equations we created.
M - 2d = 58 becomes M - (2)(8) = 58
Simplify: M - 16 = 58
Solve: M = 74

ASIDE: We have 2 free videos on standard deviation:
Part I: https://www.gmatprepnow.com/module/gmat- ... ics?id=806
Part II: https://www.gmatprepnow.com/module/gmat- ... ics?id=809

[OptimusPrep]

If two deviations down the mean is 58 and three up is 98. What is the mean?

Please help

Standard deviation is nothing, but the how far you actually are from the mean.

So here if we assume mean to be M and standard deviation to be D.
We can form the following equations:

M-2D = 58
M+3D = 98

If we subtract the first equation from the second, we get 5D = 40
or D = 8

Putting this value of D in equation 1, we get
M-16 = 58,
Hence M = 74

[nikhilgmat31]

m - 2d = 58
m +3d = 98
5d = 40
d = 8

m=74