# What would the calculated value of the standard deviation of a uniform distribution be?

A colleague wants to compare models that use either a Gaussian distribution or a uniform distribution and for other reasons needs the standard devation of these two distributions to be equal. In R I can do a simulation...

sd(runif(100000000))
sd(runif(100000000,min=0,max=2))


and see that the calculated standard deviation is likely to be ~.2887 * the range of the uniform distribution. However, I was wondering if there was an equation that could yield the exact value, and if so, what that formula was.

• What is "not meaningful" about the standard deviation of a uniform distribution? It is a measure of spread for the uniform, just as it is for almost every other distribution. It may not be the best measure of spread, but it is certainly meaningful. Jul 29 '10 at 23:32
• All I meant was that the standard deviation is not really a parameter that defines or describes the uniform distribution well. In my mind, the standard deviation refers to the spread of a normal, or near normal distribution. Simply because a value is calculable does not mean that it is interesting or meaningful. For example, I might be able to calculate what rate parameter from an exponential distribution best matches a normal distribution, but to me such a value would not be particularly meaningful because the distribution being described is not actually exponential. Jul 30 '10 at 6:51
• I can define a uniform distribution with mean 0.5 and standard deviation 1/12. It is perfectly well defined, but it is not the most natural parameterization. There is nothing about standard deviations that implies normality. Jul 30 '10 at 11:36