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:
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.