Frequency, Relative Frequency, Cumulative Frequency, and Cumulative Relative Frequency
July 10, 2026
The four columns that turn raw numbers into a table
A frequency distribution table takes a pile of numbers and sorts them into classes, then counts how many land in each one. Most tables show four counts side by side: frequency, relative frequency, cumulative frequency, and cumulative relative frequency. Each one answers a different question, and together they give you a full picture of how your data spreads out.
Let's walk through all four with a real example.
The dataset
Say you collected the ages of 20 people. That is your sample, so n = 20. The youngest and oldest are 40 apart, which gives a range of 40. The mean age is 42.8 and the median is 43.
To build the table, you split that range into classes. Sturges' rule points to 6 classes for a sample this size, so each class covers an equal-width slice of the range. That gives you the six age bands you see below.
The full table
| Class (age) | Frequency | Relative frequency | Cumulative frequency | Cumulative relative frequency |
|---|---|---|---|---|
| 23 to 29.67 | 3 | 15% | 3 | 15% |
| 29.67 to 36.33 | 4 | 20% | 7 | 35% |
| 36.33 to 43 | 3 | 15% | 10 | 50% |
| 43 to 49.67 | 4 | 20% | 14 | 70% |
| 49.67 to 56.33 | 3 | 15% | 17 | 85% |
| 56.33 to 63 | 3 | 15% | 20 | 100% |
Now let's read each column.
Frequency: the raw count
Frequency is the plain count of how many values fall into a class. Nothing fancy. Look at the first row: 3 people are aged 23 to 29.67. The second class holds 4 people, and so on down the table.
If you add every frequency together, you get back the sample size. Three plus four plus three plus four plus three plus three lands on 20, which is exactly how many people you started with. That check is worth doing every time. If the frequencies don't sum to n, a value got miscounted or dropped.
Frequency alone is what a plain histogram plots. The height of each bar is the count for that class. You can build one from this same data on the histogram maker and see the shape right away.
Relative frequency: the share of the whole
Relative frequency turns each count into a proportion. The formula is simple:
Relative frequency = frequency / total
So the first class, with 3 out of 20, works out to 15%. The second class, 4 out of 20, is 20%. Every row in the table is that same division, written as a percent.
The useful property here is that all the relative frequencies add up to 100 percent. Fifteen plus twenty plus fifteen plus twenty plus fifteen plus fifteen comes to 100. That makes sense, since every person has to fall into exactly one class, and the whole sample accounts for the whole 100 percent.
Relative frequency is what lets you compare two datasets of different sizes. A raw count of 4 means little on its own, but "20 percent of the sample" is something you can hold next to another group. When you want the bars to show shares instead of counts, plot a relative frequency histogram instead of a plain one.
Cumulative frequency: the running total
Cumulative frequency is a running total of the frequency column. You carry the count forward as you go down the classes.
Start at the top with 3. Add the next class of 4 and you are at 7. Add the following 3 and you reach 10. Keep going: 14, then 17, then 20. Each cumulative value tells you how many people fall at or below the top of that class.
That is why the last cumulative value lands on 20, the sample size. By the final class you have accounted for everyone, so the running total has to equal n. If your bottom cumulative number is anything other than the sample size, something upstream is off.
Cumulative frequency is handy for "how many are under X" questions. Reading the table, 10 people are aged 43 or younger, since the median sits at 43 and the cumulative count hits 10 at that boundary. You can pull answers like that straight off the column without recounting anything.
Cumulative relative frequency: the running share
This is the fourth column, and it is the one people ask about most. Cumulative relative frequency is the running total written as a percentage instead of a count. It answers "what share of the data falls at or below here."
There are two ways to work it out, and they always agree.
Cumulative relative frequency = cumulative frequency / total
Take the third class. Its cumulative frequency is 10, and 10 out of 20 is 50 percent. Done.
Or: add up the relative frequencies as you go
Start with 15 percent. Add the next class at 20 percent and you have 35. Add 15 and you reach 50. Keep going: 70, then 85, then 100.
Both routes land on the same six numbers, which is a useful check. If adding the percentages down the column gives you something different from dividing the cumulative count by n, one of the two columns has an arithmetic slip in it.
The last value has to be 100 percent, for the same reason the last cumulative frequency has to equal the sample size. By the bottom row you have accounted for everyone.
What makes this column worth the extra step is that it reads like a percentile. Half the group is 43 or younger, since the running share hits 50 percent at that class boundary. Eighty-five percent are under 56.33. Those are statements you can make about a sample of 20 or a sample of 20,000 in exactly the same words, which is not true of the raw cumulative count.
The histogram maker builds this column for you. Its output table carries the count, the relative percentage, and the cumulative percentage for every bin, and that last column is this one: a running share that ends at 100 percent.
Worth knowing before you copy numbers out of either tool, because the two label things differently. The frequency distribution table maker reports its cumulative column as a running count, ending at n. The histogram maker reports its cumulative column as a running percentage, ending at 100. Same idea, different units, and which one you want depends on whether you are answering "how many" or "what share". Check the last row before you trust a cumulative column you did not build yourself.
Which column answers which question
The four columns get confused with each other constantly, mostly because the names overlap. The difference is easier to hold onto as a pair of questions: count or share, and this class only or everything so far.
| Column | Count or share? | This class or running total? | The question it answers |
|---|---|---|---|
| Frequency | Count | This class | How many landed in this class? |
| Relative frequency | Share | This class | What percent of the data is in this class? |
| Cumulative frequency | Count | Running total | How many are at or below this class? |
| Cumulative relative frequency | Share | Running total | What percent are at or below this class? |
A few specific comparisons that come up a lot:
Frequency vs relative frequency. Same information, different units. Frequency is 3 people, relative frequency is 15 percent of the sample. Frequency is sometimes called absolute frequency to make the contrast explicit. Use relative frequency when you need to compare two groups of different sizes, because a count of 3 means nothing next to a count of 300 until you know how big each sample was.
Cumulative frequency vs cumulative relative frequency. Again the same running total, once as a count and once as a share. Cumulative frequency ends at n. Cumulative relative frequency ends at 100 percent.
Frequency histogram vs relative frequency histogram. Same bars, same shape, different y-axis. One is labelled in counts and the other in percentages, and the bars keep their proportions either way. That is why switching between them on a chart changes the axis labels and nothing else. The relative frequency histogram page covers when each one is the right choice.
Putting it together
Each column builds on the one before it. Frequency counts. Relative frequency scales that count against the total. Cumulative frequency stacks the counts up. Cumulative relative frequency stacks the shares up. Three quick checks keep you honest: the relative frequencies should total 100 percent, the last cumulative frequency should equal the sample size, and the last cumulative relative frequency should be 100 percent. All three hold in the table above.
You don't have to grind through the arithmetic by hand. Paste your numbers into the frequency distribution table maker and it builds the classes, the frequency, the relative frequency, and the cumulative frequency for you. If you want the running share instead of the running count, the histogram maker reports the same column as a percentage. From there you can chart the same data on the histogram maker to see the distribution take shape, and if you are still deciding how many classes to use, the guide on how to choose bins walks through the trade-offs.