There are various guidelines when picking the number of bins, where k is the number of bins and n is the range. The number of bins, k, can be calculated from a suggested bin width h as follows:

h = $⌈\frac{\mathrm{maximum}- \mathrm{minimum}}{h}⌉$,

where the braces indicate the ceiling function.

Square-root choice: The simplest method of deciding on the number of bins is to take square root of the number of data points.

k = $\sqrt{\mathit{n}}$

Sturges' formula: Sturges' Formula is derived from a binomial distribution and assumes that the data is normally distributed. Sturges' formula has been known to perform poorly in some cases if n is less than 30 and if the data is not normally distributed.

k = $⌈{\log }_2\mathit{n} \+ 1⌉$

Scott's normal reference rule: Scott's normal reference rule minimizes the integrated mean squared error of the density estimate and is well suited for random samples of normally distributed data.

h = $\frac{3.5 \stackrel{\^}{\mathrm{\σ}}}{n^{\frac{1}{3}}}$,

where $\stackrel{\^}{\mathrm{\sigma }}$ is the sample standard deviation.

Freedman-Diaconis' choice: The Freedman-Diaconis' choice is based on the interquartile range (IQR). It is less sensitive to outliers in data than Scott's normal reference rule because of using the interquartile range.

h = $\frac{2 \mathrm{IQR}\left(\mathrm{Sample}\right)}{n^{\frac{1}{3}}}$