ARZENTIQ
SCIENCE & MATHS

Histogram & Frequency Table

Turn numbers into a histogram and frequency table — bins by Sturges, Rice, Scott or Freedman–Diaconis, or your own width or count — with cumulative frequencies.

A bar chart, a frequency table (count, relative, cumulative per bin), the bin width and rule used, and summary statistics (n, min, max, mean, sd, IQR).

Example: 1 2 2 3 3 3 4 4 5 9 → Sturges gives 5 bins of width 2 from 0: [0,2) 1, [2,4) 5, [4,6) 3, [6,8) 0, [8,10] 1 — the empty bin is flagged; try width 3 or Freedman–Diaconis.

v0.1.0 · last reviewed 21 September 2026
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Choose the bins,
show the shape.

How bin width is chosen by each rule, how values are counted, and why the rules disagree.

The rules

Sturges gives ⌈log₂n + 1⌉ bins — fine for near-normal data of modest size. Rice gives ⌈2·n^(1/3)⌉. Scott sets the width to 3.49·s·n^(−1/3) from the standard deviation; Freedman–Diaconis sets it to 2·IQR·n^(−1/3), which resists outliers. The page rounds a rule’s width to a 1-2-2.5-5 step so the edges read cleanly, or takes the width or count you enter exactly.

Counting

Bins run from a start (the rule’s rounded-down minimum, or yours) in equal steps; each bin is [lower, upper) — a value on an edge goes to the upper bin — except the last, which is closed so the maximum is counted. The table gives count, relative frequency, cumulative count and cumulative share; the chart highlights the modal bin.

Reading it

Different rules give different pictures of the same data; none is wrong. Too many bins show noise, too few hide structure — try two. Empty bins are flagged. Summary statistics (mean, sample sd, IQR) sit alongside so the shape and the numbers agree. Nothing leaves the browser; the same four anonymous usage counts as the rest of the site apply.

SOURCES

  • Bin rules: Sturges ⌈log₂n + 1⌉, Rice ⌈2n^(1/3)⌉, Scott 3.49·s·n^(−1/3), Freedman–Diaconis 2·IQR·n^(−1/3); rule widths rounded to a 1-2-2.5-5 step; bins [lower, upper) with the last closed

Last reviewed 21 September 2026. How results are checked: How we verify.