A histogram has one setting nobody votes on: how wide the bins are. Change not a single data value, drag that width, and the same numbers can look smooth, spiky, two‑humped or flat. Every bar below is counted live from the values actually on screen — so you can watch the shape move while the data holds still.
The histogram
The same data at six bin widths
Same n values, same sample, six widths. Nothing changed but the bins. Tap a panel to load that width above.
Choosing the bin widthdrag the width slider
4 bpm
0% of h
150
Values n150
Width h4
Bins k15
Peaks seen1
Rules of thumb — computed from these values, tap to apply
The rules disagree on purpose. The square-root and Sturges rules pick a number of bins from n alone and then split the range; Sturges was derived for roughly normal data and tends to under-bin large samples. Scott and Freedman–Diaconis pick a width from how spread out the data actually are, shrinking it like 1/∛n — four times the data buys you only about a 60% narrower bin. Freedman–Diaconis uses the IQR instead of the standard deviation, so one wild outlier cannot inflate it. All four assume a single smooth hump; none of them knows your data have two.
Always report the bin width. A histogram is one view of the data at one resolution, chosen by whoever drew it. Before you believe a feature — a second hump, a gap, a spike — check it at two or three widths and in a fresh sample. Structure that is genuinely in the population survives that test. Structure manufactured by the bins does not.