Frequency Distribution Calculator
Turn a list of values into a frequency table — counts, relative frequencies and cumulative frequencies, in classes chosen for you or by you.
The range is divided into equal-width classes and each value is counted into one.
How the frequency distribution calculator works
The range is divided into equal-width classes and each value is counted into one. The default class count follows Sturges' rule, ⌈log₂ n⌉ + 1, which is the conventional starting point.
Class width is the real decision: too few classes hide the shape, too many turn the histogram back into the raw data. There is no correct answer, only a readable one.
Formula: classes = ⌈log₂ n⌉ + 1; width = range / classes
Worked examples
| Inputs | Classes used | Note |
|---|---|---|
| Fifteen values | 5 | Sturges gives 5 classes |
| Four classes | 4 | wider bins, smoother shape |
| Ten classes | 10 | finer, noisier |
FAQFrequently asked questions
How many classes should I use?
Sturges' rule, ⌈log₂ n⌉ + 1, is the usual starting point. For large or skewed samples the Freedman–Diaconis rule based on the IQR often reads better.
What is relative frequency?
The count in a class as a share of the total — what makes tables from different sample sizes comparable.
What is cumulative frequency?
A running total. It answers "how many are below this point?" and its plot is the empirical CDF.
Does the class width matter?
Enormously. The same data can look bimodal, uniform or bell-shaped depending on the bins — which is a good reason to look at the raw data too.
What is the modal class?
The class with the most values. It is not the mode of the data, which depends on where the boundaries happen to fall.
Where these figures come from
- NIST Digital Library of Mathematical Functions — reference definitions for elementary and special functions
- Wolfram MathWorld — definitions and formulas for every topic on this page
- NIST/SEMATECH e-Handbook of Statistical Methods — the statistical formulas (mean, variance, z, confidence intervals, sample size)
- Common Core State Standards — Mathematics — the terms and methods taught in US schools
Last checked: September 2026. Formulas are fixed by mathematics and do not change with tax years or regulations.