MAD versus Standard Deviation for a Uniform Distribution

In my last post, I talked about the relationship between the mean absolute deviation (MAD) and standard deviation (STDEV) for a normal distribution. Apparently, many people had never seen the math behind it, and I got questions about the same relationship for the case where the demand was not normally distributed. In this post, I am going to derive the same for a uniform distribution.

Say X is a uniformly distributed random variable between limits a and b. Then:

By symmetry, the two integrals are equal, so we can just evaluate:

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MAD = (b – a)/4

The ratio of MAD to standard deviation is:

Thus, MAD ≈ 0.866 (ST DEV)

Or ST DEV ≈ 1.155 (MAD)

By referencing the previous blog, we can see that the relationship between MAD and Standard Deviation for a normal distribution is:

ST DEV ≈ .1.25 (MAD)

This goes to show that the underlying distribution matters and one should not blindly use one value to estimate the relationship between the two.

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