What this calculator does
Relative frequency is how large a share of the total each category takes up, once every category's raw count has been divided by the grand total. A raw count of 18 means little without knowing what it is 18 out of; a relative frequency of 36 per cent says exactly that.
This calculator takes a list of raw counts, one per category, and returns each category's relative frequency alongside its cumulative relative frequency, the running share accounted for by that category and every one before it. Cumulative relative frequency is what a relative frequency table or ogive is normally built from.
The formula
Each category's relative frequency is its own count divided by the sum of all the counts entered. Cumulative relative frequency adds each category's share to the running total of every category before it, so the last category always reaches exactly 100 per cent.
| Term | Meaning |
|---|---|
| Relative frequency | A category's count divided by the total of all counts. |
| Cumulative relative frequency | The running total of relative frequency, up to and including the current category. |
| Frequency | The raw count for a category, before it is expressed as a share of anything. |
The inputs explained
| Field | What to enter |
|---|---|
| Category counts (comma or space separated) | The raw count for each category, in order, separated by commas or spaces. The categories themselves are not named, just numbered in the order entered. |
When to use it
Summarising a tally or survey
A tally of responses by category converts directly into relative frequencies, which are easier to compare across groups of different total sizes than the raw counts are.
Building a relative frequency table for coursework
Statistics courses commonly ask for a table of frequency, relative frequency and cumulative relative frequency together; this calculator produces the latter two directly from the raw counts.
Checking which category dominates
The largest single share and the point where the cumulative total crosses 50 per cent are both quick ways to see which categories carry most of the data.
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
Relative frequency for a small set of category counts
A short list of category counts, shown as relative frequency.
| Category counts | Total observations | Largest category share |
|---|---|---|
| 12, 18, 7, 3 | 40 | 45.0% |
| 10, 10, 10, 10 | 40 | 25.0% |
| 50, 5, 5, 40 | 100 | 50.0% |
| 1, 2, 3, 4 | 10 | 40.0% |
Questions
Does relative frequency have to add up to 100 per cent?
Yes, across all categories entered. That is what the final row of the cumulative relative frequency column shows, and it is a useful check that no category was left out.
Can relative frequency be used to estimate probability?
Yes, this is the empirical or experimental approach to probability: treating each category's relative frequency in an existing data set as an estimate of the probability of that outcome occurring, given enough observations.
What is the difference between relative frequency and grouped frequency?
Relative frequency works directly from raw category counts, as here. Grouped frequency starts from class intervals and midpoints for continuous data that has first been binned into ranges, which is a different calculation.
Do the categories need labels?
Not for the maths. This calculator numbers the categories in the order the counts are entered; add your own category names when transcribing the result into a table or report.
For frequency data already grouped into class intervals, see the grouped frequency statistics calculator.