Editing Histogram (section)

==== Remark ====

A good reason why the number of bins should be proportional to <math>\sqrt[3]{n}</math> is the following: suppose that the data are obtained as <math>n</math> independent realizations of a bounded probability distribution with smooth density. Then the histogram remains equally "rugged" as <math>n</math> tends to infinity. If <math>s</math> is the "width" of the distribution (e. g., the standard deviation or the inter-quartile range), then the number of units in a bin (the frequency) is of order <math>n h/s</math> and the ''relative'' standard error is of order <math>\sqrt{s/(n h)}</math>. Compared to the next bin, the relative change of the frequency is of order <math>h/s</math> provided that the derivative of the density is non-zero. These two are of the same order if <math>h</math> is of order <math>s/\sqrt[3]{n}</math>, so that <math>k</math> is of order <math>\sqrt[3]{n}</math>. This simple cubic root choice can also be applied to bins with non-constant widths.{{cn|date=May 2024}}

[[File:Gumbel distribtion.png|thumb|300px|Histogram and density function for a [[Gumbel distribution]]<ref>[https://www.waterlog.info/cumfreq.htm A calculator for probability distributions and density functions]</ref>]]