Frequency Distribution Calculator

What the frequency distribution calculator does

A frequency distribution counts how many times each value appears in your data, turning a long list into a short, readable table. This calculator builds that table for you, adds a running cumulative count, draws both as bar charts, and throws in a full set of summary statistics alongside.

It is often the first thing you do with a fresh set of numbers, because seeing which values are common and which are rare tells you the shape of the data at a glance. Below is how it works.

How to use it

1. Enter your dataset in the box, separated by commas, spaces, or new lines.
2. Press Calculate for the frequency table, the charts, and the summary statistics, or Reset to clear it.

How the table is built

The calculator sorts your data and then tallies it, going through the values and counting how many times each distinct one appears. Each unique value becomes a row, and its count is its frequency. The frequencies always add up to the total number of values you entered, which is a handy check that nothing was missed.

This is an ungrouped frequency distribution, meaning it counts each individual value on its own rather than lumping values into ranges. That is exactly what you want when your data takes a limited set of distinct values, like dice rolls, ratings, or counts.

Frequency and cumulative frequency

Alongside the plain frequency, the calculator gives the cumulative frequency, which is a running total. Each value's cumulative frequency is its own count plus the counts of everything below it, so the numbers climb as you go down the table and reach the full data size at the bottom.

The two answer different questions. The frequency tells you how many values equal a given number, while the cumulative frequency tells you how many are at or below it. That running total is the quick way to ask things like how many values fall under a threshold, without counting them again by hand.

When to group your data

Counting each distinct value works beautifully until there are too many of them. If your data is spread across a wide range with few repeats, like measured heights or times, an ungrouped table would have a row for almost every value and tell you very little.

In that case the answer is to group the data into classes, equal-width ranges that you count into instead of single values. Choosing how wide those ranges should be is its own small task, and our class width calculator handles it, giving you the bin size to build a grouped table or a histogram from.

A worked example

Take the seven values 4, 5, 5, 6, 6, 6, 7. Counting each one gives the frequency table: 4 appears once, 5 appears twice, 6 appears three times, and 7 appears once.

The cumulative frequencies build from the top: 1, then 1 plus 2 is 3, then 3 plus 3 is 6, then 6 plus 1 is 7, the full count. So four of the seven values are 6 or below, which the cumulative column tells you at a glance.

Entering your data, and the extras

You can separate your numbers with commas, spaces, or new lines, in any mix, and the calculator sorts them for you. Besides the table and its two bar charts, it reports a full summary of the data, the minimum, maximum, range, count, sum, mean, median, standard deviation, and variance, so you get the distribution and its key numbers in one go. The standard deviation and variance here use the population formulas.

Questions people ask

What is a frequency distribution?

A table that shows how many times each value appears in a data set. It summarises a long list of numbers into counts per value.

What is cumulative frequency?

A running total of the frequencies. Each value's cumulative frequency is its count plus the counts of all smaller values, so it tells you how many values are at or below that point.

Does this group data into ranges?

No, it counts each distinct value on its own. For data spread over a wide range, group it into classes instead, using the class width calculator to size the ranges.

Should the frequencies add up to anything?

Yes, to the total number of values you entered. If they do not, a value was missed, which makes the total a useful check.

References

A quick note on where the methods here come from. Frequency distributions and cumulative frequency are set out in the NIST/SEMATECH e-Handbook of Statistical Methods, the US government's public statistics reference. OpenStax Introductory Statistics is a free, widely used textbook that covers frequency tables and how to read them.

1. NIST/SEMATECH e-Handbook of Statistical Methods (frequency distributions and exploratory data analysis). https://www.itl.nist.gov/div898/handbook/
2. OpenStax, Introductory Statistics (frequency, frequency tables, and levels of measurement). https://openstax.org/details/books/introductory-statistics-2e