Question

I don’t know anything about statistics and it was difficult for me to find A way to describe my question that was clear.

I am doing some initial research on a system that will measure the uniformity of electricity across a conductor. Basically we need to measure how evenly a signal is spread out on a surface.

I was doing research on how to determine uniformity of a data set and came across this question which is promising. However I realized that I don’t know what unit to use to express uniformity. For example, if I take 100 equally spaced measurements in a grid pattern on the surface of an object and want to describe how uniform the values are, how would you say it?

• “98% uniform?” – what does that mean? 98% of what?
• “The signal is very evenly dispersed” – OK, great… but there must be a more specific or scientific way to communicate that… how “evenly”? What is a numeric representation of that statement?

Statistics and math are not my thing so if this seems like a dumb question, be gentle…

Answer 1

You are looking for the Variance. From Wikipedia:

In probability theory and statistics, the variance is a measure of how far a set of numbers are spread out from each other. It is one of several descriptors of a probability distribution, describing how far the numbers lie from the mean

Recipe for calculating the Variance:

1) Calculate the Mean of your dataset

2) For each point, calculate (X – Mean)^2

3) Add up all those (X – Mean)^2

4) Divide the by the number of points

5) That is it

The Variance gives you an idea of how “equal” your points are. A Variance of zero, means all points are equal, and then increases as the points spread out.

Edit

Here you may find better algorithms (more numerically stable) for calculating the variance.