Relative Frequency Calculator
Enter your raw frequency counts (or individual data values) and get a full relative frequency distribution: proportions, percentages, cumulative counts, cumulative percents, the mode, and the weighted mean, all in one table you can sort and copy.
Formula
Worked example
For frequencies 8, 12, 15, 9, 6 the total n = 50. Class 3 has f = 15: relative frequency = 15/50 = 0.3000, percent = 30.0%. The cumulative frequency after class 3 is 8 + 12 + 15 = 35, and the cumulative percent is 35/50 = 70.0%. The mode is Class 3 (highest frequency). The relative frequencies 0.1600, 0.2400, 0.3000, 0.1800, 0.1200 sum to 1.0000.
What relative frequency means and why it matters
The frequency of a class is how many observations fall into it. The relative frequency rescales that count against the whole data set by dividing by the total n. The result, a proportion between 0 and 1, answers "what share of everything landed here?" Because every class uses the same denominator, relative frequencies let you compare data sets of very different sizes on equal footing. A count of 30 means something quite different in a sample of 40 than in one of 4,000, but a relative frequency of 0.30 carries the same meaning in both. Multiply by 100 to express it as a percent; the percent column and the proportion column hold identical information in two scales.
Cumulative frequency and the cumulative percent column
A cumulative frequency is the running total of observations from the first class through the current one. The cumulative relative frequency (or cumulative percent) is that running total divided by n. The last row always equals n and 100%. This column lets you answer "at or below" questions directly from the table: the cumulative percent up through a given class is the fraction of the data that falls at or below that class, which is the definition of a percentile. If the cumulative percent at class 3 is 70%, then 70% of all observations are in classes 1, 2, or 3. Ogive charts (cumulative frequency curves) are built by plotting cumulative percent against the class boundaries.
Mode, mean, and interpreting the distribution
The mode is simply the class with the highest frequency; it is always the tallest bar in a frequency histogram. When there are two equally dominant classes the distribution is called bimodal. The weighted mean of the distribution is calculated as the sum of each class value times its relative frequency, which gives the average of the distribution. If your class labels are categories rather than numbers (for example survey responses), the mean is not meaningful and only the mode and relative frequencies apply. A relative frequency distribution is also the backbone of probability: if the data represent random outcomes, each relative frequency is an estimate of that outcome's probability.
Raw data vs. pre-counted frequencies
This calculator accepts two kinds of input. If you already have a frequency table, choose "Pre-counted frequencies" and type the counts directly. If you have individual observations, such as survey responses or test scores, choose "Raw data list" and paste all the values in. The calculator tallies how often each unique value appears and builds the full distribution for you. Optional class labels let you name the categories (for example Mon, Tue, Wed) when working with non-numeric data. The sort control re-orders the table by frequency or original order without changing any of the numbers.
Worked relative frequency distribution
| Class | Freq. (f) | Rel. freq. | Percent | Cumul. f | Cumul. % |
|---|---|---|---|---|---|
| 1 | 8 | 0.1600 | 16.0% | 8 | 16.0% |
| 2 | 12 | 0.2400 | 24.0% | 20 | 40.0% |
| 3 | 15 | 0.3000 | 30.0% | 35 | 70.0% |
| 4 | 9 | 0.1800 | 18.0% | 44 | 88.0% |
| 5 | 6 | 0.1200 | 12.0% | 50 | 100.0% |
| Total | 50 | 1.0000 | 100.0% | 50 | 100.0% |
Five classes with frequencies 8, 12, 15, 9, 6 (n = 50). Cumulative columns run left to right.
Frequently asked questions
What is the formula for relative frequency?
Divide a class frequency f by the total number of observations n: relative frequency = f / n. The result is a proportion between 0 and 1. Multiply by 100 to express it as a percentage. Every class in the distribution uses the same denominator, so the values all sum to 1 (or 100%).
Should relative frequencies add up to 1 or 100%?
Both: they are the same statement in different scales. As proportions they sum to exactly 1.0000; as percentages they sum to 100%. A total that misses this slightly is usually just rounding. A large gap means an observation was either dropped, counted twice, or placed in more than one class.
What is cumulative relative frequency?
Cumulative relative frequency is the running total of relative frequencies from the first class through the current class. At any class it tells you what fraction of all observations fall at or below that class. The cumulative relative frequency of the last class is always 1.0 (100%). It is the basis of ogive (cumulative frequency) charts and percentile lookups.
What is the difference between frequency and relative frequency?
Frequency is the raw count of observations in a class. Relative frequency is that count divided by the total n, giving a share between 0 and 1. Relative frequency makes data sets of different sizes directly comparable, which raw counts cannot do alone.
How do I find the mode from a frequency table?
The mode is the class with the highest frequency. In the relative frequency distribution it also has the highest relative frequency and the tallest bar in a histogram. If two classes tie for the highest frequency the distribution is bimodal; if all classes have equal frequencies there is no mode.
Can I enter raw data instead of pre-counted frequencies?
Yes. Switch the input method to "Raw data list" and paste individual observations separated by commas or spaces, for example the test scores for a whole class. The calculator tallies each unique value automatically and builds the full relative frequency table for you.