Histogram Bin Calculator

Because they use different information: Sturges', Square Root, and Rice rules look only at how many data points you have, while Scott's and Freedman-Diaconis also factor in how spread out the data is (via the interquartile range). A dataset with the same sample count but a wider spread will get a wider recommended bin width and fewer bins from Scott's or Freedman-Diaconis, but the identical answer from the three count-only rules.

Freedman-Diaconis is the most robust to outliers among the five, because it bases its bin width directly on the interquartile range (the middle 50% of your data), which barely moves even if a few extreme values are added or removed. Rules based on standard deviation, like Scott's, or on sample count alone can be more distorted by extreme values sitting far from the bulk of the distribution.

Yes, for every one of these five rules, holding the data's range and spread constant -- more data points support finer resolution without individual bins becoming too sparse to be meaningful. The relationship is not linear, though: most of these formulas grow with the cube root or logarithm of sample count, so doubling your data does not double the recommended bin count.

Data Range (maximum minus minimum) sets how wide the whole histogram needs to span, while IQR (the spread of just the middle 50% of the data) is used only by Scott's and Freedman-Diaconis rules to estimate the data's typical spread for bin width. A dataset can have a huge range dominated by a few extreme outliers while its IQR stays modest, which is exactly the situation Freedman-Diaconis is designed to handle well.

Scott's Rule still runs, but its spread estimate comes entirely from dividing your entered IQR by 1.35 to approximate a standard deviation, so an inaccurate IQR will produce an inaccurate bin width recommendation for this method specifically. If you don't have a real IQR handy, Sturges' Rule or the Square Root Rule -- which need only your sample count -- are more reliable fallbacks.