Wikipedia:Reference desk/Archives/Mathematics/2024 April 27

= April 27 =

"Distribution diagrams"
I'm trying to show the distribution characteristics of a numerical value in a (finite) population. To do so, I sort the values in ascending order, and then plot the feature values over the position of the value in the sorted sequence, as per the attached example. I'm probably not the first with that idea - is there a standard name for this kind of diagram? And/or is there a better way to visualise such data? --Stephan Schulz (talk) 13:36, 27 April 2024 (UTC)


 * If you switch axes (or turn your head sideways) this is the graph of a typical Cumulative distribution function. Perhaps it's better to call it a cumulative frequency instead of a distribution since you're plotting values observed and not the theoretical probability density, but the idea is the same. In particular, your graph resembles the second image shown in the article only turned sideways. The (usual) probability density is simply the derivative of the cumulative distribution function, so if you can estimate the derivative in your diagram that may give a better visual representation. The usual technique is to divide the range in to intervals, and then graph the number of occurrences in each interval. It seems to me that there might be a name in economics for the "sideways" version (enonomists seem to do a lot of things sideways), but I don't know what it would be. --RDBury (talk) 14:41, 27 April 2024 (UTC)
 * It is also customary, when plotting a cumulative distribution, to let the (now vertical) axis mark relative values in the range from 0 to 1 (or, equivalently and perhaps more commonly, from 0% to 100%) instead of an absolute ranking like from 1 to 7794 or whatever the sample size may be. --Lambiam 15:06, 27 April 2024 (UTC)
 * See also Empirical distribution function and Quantile function. —Amble (talk) 00:13, 30 April 2024 (UTC)