24 students took the test in your class, and 16 in the class next door. If both classes have exactly 6 students scoring "90 or above," which class did better? Looking only at frequency (headcount), both look the same at 6 students, but it's actually a completely different story. Your class has 6 out of 24 (25%), while the other class has 6 out of 16 (37.5%). The other class's share scoring 90 or above is actually much higher.
The share that one class's frequency takes up of the total frequency, like this, is called relative frequency. The calculation is simple.
Let's redo the calculation from our example. Your class's relative frequency for "90 or above" is 6 ÷ 24 = 0.25, and the other class's is 6 ÷ 16 = 0.375. The frequency was the same, 6 students, but switching to relative frequency makes the difference between the two classes crystal clear.
| Class | Your class (24) frequency | Your class rel. freq. | Other class (16) frequency | Other class rel. freq. |
|---|---|---|---|---|
| 90 or above | 6 | 0.25 (25%) | 6 | 0.375 (37.5%) |
Relative frequency has one interesting property: add up the relative frequencies of every class in a single group, and it always comes to 1 (=100%). That's because adding up the frequencies of every class ultimately equals the total frequency. So if the relative frequencies don't add up to 1, you immediately know a calculation went wrong somewhere — a handy property for checking your work.
Relative frequency really shows its worth when comparing groups whose sizes (total frequency) differ. Comparing your school's tardiness rate to another school's, or comparing some percentage between your country and a country with a different population — comparing the raw numbers (frequencies) as-is is unfair, since the bigger group will generally have a bigger frequency regardless. Switch to relative frequency, and you get a common yardstick — "what percent of the whole" — letting you fairly compare groups of different sizes.
On our activity page, you can generate scores for two classes with different numbers of students, and press the "Compare by frequency" and "Compare by relative frequency" buttons to see just how differently the two graphs look. On the frequency graph, the class with more students generally shows taller bars, but switch to the relative frequency graph and the real difference in proportions comes out.