The uniform distribution calculator works out standard deviation, p(x1≤ x ≤ x2) and variance from parameter (a), parameter (b), x, x1, x2, quantile (p) and one way. Enter what you have and the relationship is applied straight away, so you get the answer without working through the algebra yourself.
What Is the Uniform Distribution Calculator?
The uniform distribution calculator turns a set of measurements into standard deviation, p(x1≤ x ≤ x2) and variance, with the uncertainty made explicit rather than left implied.
Statistics is easy to quote badly. A figure without its spread tells the reader far less than they assume it does, and this calculator puts both together.
How the Uniform Distribution Is Calculated
The calculation uses the standard relationship for this kind of estimate, applied to the figures you supply. The intermediate steps are exposed so you can see how much of the answer comes from each one.
Sample size matters more than most people expect. Doubling the number of observations improves the precision by a factor of about one and a half, not two.
What the Result Does and Does Not Tell You
A result describes the data you gave it. It does not tell you whether the sample was representative, whether the method was appropriate, or whether there is a confound in the way the figures were collected.
Report the result together with its uncertainty. A number on its own is much easier to misread than a number with a range attached.
A Worked Example
Working through an example, with parameter (a) set to 10, parameter (b) set to 5, x set to 2, the calculator returns mean of 7.5, and variance of 2.08333, and median of 7.5. Substitute your own figures and the same steps produce the same kind of answer.
Frequently Asked Questions
What do I need to work out standard deviation?
Enter parameter (a), parameter (b), x, x1, x2, quantile (p) and one way. The calculator then works through the relationship and reports standard deviation, p(x1≤ x ≤ x2) and variance.
What does the uniform distribution actually calculate?
It takes parameter (a), parameter (b), x, x1, x2, quantile (p) and one way and converts them into standard deviation, p(x1≤ x ≤ x2) and variance using the standard relationship for this problem. Each step is applied in turn, so every output is traceable back to the numbers you typed in.
How should I enter parameter (a)?
Use the value you actually have, in the unit shown next to the field. Enter every value in the same unit system. The calculator assumes the figures you supply are consistent, so it cannot correct a mistake that happens before the calculation starts.
Can I use this for a quick estimate as well as a precise answer?
Yes. The calculator is built for quick checks, so round your inputs to a sensible number of significant figures and the result will be just as useful. If you need more precision, keep the same method and add digits to the inputs rather than adjusting the method itself.
Is the answer exact?
It is as exact as the formula and the inputs allow. The method itself is the standard one for this problem, so the only sources of error are the figures you enter and the precision you ask for.