astropy.stats.scott_bin_width(data, return_bins=False)[source] [edit on github]

Return the optimal histogram bin width using Scott’s rule

Scott’s rule is a normal reference rule: it minimizes the integrated mean squared error in the bin approximation under the assumption that the data is approximately Gaussian.


data : array-like, ndim=1

observed (one-dimensional) data

return_bins : bool (optional)

if True, then return the bin edges


width : float

optimal bin width using Scott’s rule

bins : ndarray

bin edges: returned if return_bins is True


The optimal bin width is

\[\Delta_b = \frac{3.5\sigma}{n^{1/3}}\]

where \(\sigma\) is the standard deviation of the data, and \(n\) is the number of data points [R60].


[R60](1, 2) Scott, David W. (1979). “On optimal and data-based histograms”. Biometricka 66 (3): 605-610