Relative Frequency Calculator

What the relative frequency calculator does

Relative frequency is each value's share of the whole data set, its count divided by the total. Where a plain frequency says how many, relative frequency says what fraction. This calculator works it out for every value, adds a running cumulative share, draws both as bar charts, and reports a full summary of the data.

Turning counts into shares is what lets you compare data sets of different sizes on equal terms. 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 relative frequencies, the charts, and the summary statistics, or Reset to clear it.

How relative frequency is worked out

The calculator counts how many times each value appears, then divides each count by the total number of values:

Relative frequency = count of the value ÷ total number of values

The result is a proportion between 0 and 1, and multiplying by 100 turns it into a percentage. Because every count is divided by the same total, the relative frequencies always add up to 1, or 100 percent, across the whole data set. That is the tell-tale sign of a relative frequency table done right.

Cumulative relative frequency

The calculator also builds a cumulative relative frequency, a running total of the shares. Each value's figure is its own share plus the shares of all smaller values, so the numbers climb toward 1 and reach it at the bottom of the table.

This is the proportion of the data at or below each value, which is exactly how percentiles think. If a value's cumulative relative frequency is 0.75, then three quarters of the data sits at or below it, so the cumulative column is a direct line to questions about proportions and thresholds.

Why relative frequency is worth having

Plain counts are hard to compare when the totals differ. If one class has 20 students and another has 50, knowing that 8 and 15 respectively scored top marks does not immediately tell you which class did better. Turn those into shares, 40 percent and 30 percent, and the comparison is instant.

That is the whole value of relative frequency: it strips out the size of the data set and leaves you with proportions, which can be compared across groups, plotted together, and read as the everyday percentages people already understand.

A worked example

Take the seven values 4, 5, 5, 6, 6, 6, 7. The counts are one 4, two 5s, three 6s, and one 7, out of seven values in all.

Dividing each by 7 gives the relative frequencies: 4 is about 0.14, or 14 percent, 5 is about 0.29, 6 is about 0.43, and 7 is about 0.14. They add up to 1, as they must. The cumulative shares build up as 0.14, 0.43, 0.86, and finally 1.00, so 86 percent of the data is 6 or below.

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. Beyond the relative frequencies and their two bar charts, it reports the minimum, maximum, range, count, sum, mean, median, standard deviation, and variance, giving you the shares and the underlying numbers together. The standard deviation and variance use the population formulas.

Questions people ask

What is relative frequency?

The share of the data that each value makes up, found by dividing its count by the total. It is a proportion between 0 and 1, or a percentage when multiplied by 100.

How is it different from frequency?

Frequency is a raw count of how many times a value appears. Relative frequency is that count as a fraction of the whole, which makes data sets of different sizes comparable.

What should the relative frequencies add up to?

To 1, or 100 percent. Since every count is divided by the same total, the shares always sum to the whole.

What is cumulative relative frequency?

A running total of the shares. It gives the proportion of the data at or below each value, which is the idea behind percentiles.

References

A quick note on where the methods here come from. Relative 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 covering relative frequency tables.

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