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Relative Frequency

Relative frequency is the fraction (or proportion) of times a particular event occurs out of the total number of events. It tells you how common something is compared to everything else in your data set.

The relative frequency of an event is calculated by dividing the frequency of that event by the total number of observations or trials. Relative frequencies always fall between 0 and 1 (inclusive), and the relative frequencies of all possible outcomes in a data set sum to 1. When expressed as a percentage, relative frequencies range from 0% to 100%.

Key Formula

Relative Frequency=fn\text{Relative Frequency} = \frac{f}{n}
Where:
  • ff = the frequency (count) of the event or category
  • nn = the total number of observations or trials

Worked Example

Problem: A teacher surveys 40 students about their favourite subject. The results are: Maths (12), Science (10), English (8), History (6), Art (4). Find the relative frequency of each subject.
Step 1: Identify the total number of observations.
n=12+10+8+6+4=40n = 12 + 10 + 8 + 6 + 4 = 40
Step 2: Divide each subject's frequency by the total. For Maths:
Relative FrequencyMaths=1240=0.30\text{Relative Frequency}_{\text{Maths}} = \frac{12}{40} = 0.30
Step 3: Repeat for the remaining subjects.
Science=1040=0.25,English=840=0.20,History=640=0.15,Art=440=0.10\text{Science} = \frac{10}{40} = 0.25, \quad \text{English} = \frac{8}{40} = 0.20, \quad \text{History} = \frac{6}{40} = 0.15, \quad \text{Art} = \frac{4}{40} = 0.10
Step 4: Check your work — the relative frequencies should add up to 1.
0.30+0.25+0.20+0.15+0.10=1.00✓0.30 + 0.25 + 0.20 + 0.15 + 0.10 = 1.00 \checkmark
Answer: The relative frequencies are: Maths = 0.30 (30%), Science = 0.25 (25%), English = 0.20 (20%), History = 0.15 (15%), Art = 0.10 (10%).

Visualization

Why It Matters

Relative frequency allows you to compare data sets of different sizes on equal footing. For instance, if School A surveyed 200 students and School B surveyed 500, raw counts would be misleading — but relative frequencies make comparison fair. In statistics, relative frequency from experiments also serves as an estimate of theoretical probability: the more trials you run, the closer relative frequency tends to get to the true probability.

Common Mistakes

Mistake: Using the frequency of one category as the denominator instead of the total count.
Correction: Always divide by the total number of all observations (nn), not by the count of another category. The denominator should be the sum of every category's frequency.
Mistake: Confusing relative frequency with percentage without converting.
Correction: A relative frequency of 0.30 means 30%. To convert, multiply the decimal by 100. Don't write 0.30 when the question asks for a percentage, or vice versa.

Related Terms

  • Probability — Relative frequency estimates probability experimentally
  • Histogram — Can display relative frequencies on the y-axis