Cumulative Frequency Calculator
Running totals across ordered classes — with the cumulative percentages and the interpolated median and quartiles they give.
Cumulative frequency is the running total of counts up to and including each class.
How the cumulative frequency calculator works
Cumulative frequency is the running total of counts up to and including each class. Its plot, the ogive, is the empirical distribution function.
Its main use is reading off percentiles: find the class where the running total crosses half the sample, then interpolate within it. That is how a median is estimated from grouped data.
Formula: F(i) = f₁ + f₂ + … + fᵢ
Worked examples
| Inputs | Total | Note |
|---|---|---|
| Six classes of width 10 | 40 | median about 25.4 |
| A single class | 20 | the median sits at its center |
| A symmetric table | 30 | the median lands at the middle boundary |
FAQFrequently asked questions
What is cumulative frequency?
The running total of counts up to and including each class.
What is an ogive?
The plot of cumulative frequency against the class boundaries — the empirical distribution function drawn as a curve.
How is the median interpolated?
Find the class where the running total passes half the sample, then move proportionally into that class based on how far in the halfway point falls.
Is the interpolated median exact?
No — it assumes values are spread evenly within each class. It is an estimate, and a good one when classes are narrow.
What else can I read off it?
Any percentile: find where the cumulative percentage crosses it and interpolate the same way.
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.