What is relative frequency in math?
Relative frequency is how often a value or event occurs compared with the total number of observations: frequency ÷ total. It can be a fraction, a decimal or a percent. If 12 of 40 students choose apples, the relative frequency of apples is 1240 = 0.3, or 30%. All the relative frequencies in a table add to 1.
Relative Frequency in a picture
Formal definition and notation
In a data set of n observations where a value, category or event occurs f times, its relative frequency is fn, a number from 0 to 1. A relative frequency table lists fn for every value, and the column sums to 1 (up to rounding). In a two-way table, relative frequencies can be taken over the whole table, a row or a column. In repeated trials of a chance process, the long-run relative frequency of an event gets close to its probability, which is why it is also called experimental probability.
| Symbol | Read it as | Meaning |
|---|---|---|
| f | f | the frequency: how many times the value or event occurs |
| n | n | the total number of observations or trials |
| fn | f over n | the relative frequency, often turned into a percent |
Key facts
- Relative frequencies are always between 0 and 1 (0% and 100%), and the whole table adds to 1.
- They let you compare groups of different sizes: 15 of 25 (0.6) is a bigger share than 18 of 36 (0.5), even though 18 is more than 15.
- Cumulative relative frequency adds the relative frequencies up to a value, so the last one is always 1.
- In a two-way table, a row relative frequency divides by the row total, and a column relative frequency divides by the column total. See joint frequency.
- With more trials, the relative frequency of an event usually settles close to its theoretical probability.
- A histogram or bar graph of relative frequencies has the same shape as one of counts; only the scale on the vertical axis changes.
Relative frequency formula
- f
- the count for one value or category
- n
- the total count for all values
Multiply by 100 for a percent: 1240 = 0.3 = 30%. To go back from a relative frequency to a count, multiply: 0.3 × 40 = 12.
Try it: spin and count
Spin 10 times, then 100, then 1,000. The readout shows each color’s count out of the total spins, which is its relative frequency. Watch the bars settle near the theoretical probabilities shown by the dashes.
Relative Frequency examples, step by step
Example 1: From a count to a relative frequency
A coin is flipped 50 times and lands heads 28 times. What is the relative frequency of heads?
- Relative frequency = headsflips = 2850.
- 2850 = 0.56, or 56%.
Answer: The relative frequency of heads is 0.56, or 56%.
Example 2: Build a relative frequency table
60 people were asked about their pets: dog 18, cat 12, fish 6, none 24. Find the relative frequency of each answer.
- Total: 18 + 12 + 6 + 24 = 60.
- Dog 1860 = 0.3, cat 1260 = 0.2, fish 660 = 0.1, none 2460 = 0.4.
- Check: 0.3 + 0.2 + 0.1 + 0.4 = 1.
Answer: Dog 0.3, cat 0.2, fish 0.1, none 0.4.
Example 3: Compare groups of different sizes
In Class A, 15 of 25 students ride the bus. In Class B, 18 of 36 students ride the bus. Which class has the greater relative frequency of bus riders?
- Class A: 1525 = 0.6, or 60%.
- Class B: 1836 = 0.5, or 50%.
- Class B has more bus riders, but a smaller share of its class.
Answer: Class A has the greater relative frequency, 0.6 compared with 0.5.
Common mistakes
Counts from groups of different sizes cannot be compared directly. Relative frequency puts them on the same scale.
The denominator is always the total number of observations, including the category you are counting.
Relative frequency gets close to the probability only over many trials; short runs vary a lot.
Not to be confused with
Frequency is the raw count: 12 students chose apples. Relative frequency is that count divided by the total: 1240 = 0.3.
Theoretical probability comes from the setup: a fair cube shows 6 with probability 16. Relative frequency comes from data: 18 sixes in 80 rolls is 1880 = 0.225.
A joint frequency is a count in one cell of a two-way table. Dividing it by the table total (or by a row or column total) turns it into a relative frequency.
Quick check: 3 questions
In 80 rolls of a number cube, a 6 came up 18 times. What is the relative frequency of rolling a 6?
Answer: C. 1880 = 0.225. 18 is the frequency, not the relative frequency; 0.18 treats the total as 100; 4.44 divides 80 by 18.Show answer and explanation
The relative frequencies of outcomes A, B and C are 0.25, 0.4 and x, and there are no other outcomes. What is x?
Answer: A. All the relative frequencies add to 1, so x = 1 − 0.25 − 0.4 = 0.35. 0.65 is 0.25 + 0.4, 1.35 adds 1 instead of subtracting, and 0.15 subtracts 0.25 from 0.4.Show answer and explanation
A spinner landed on red 52 times in 200 spins. About how many reds would you expect in 1,000 spins?
Answer: D. The relative frequency is 52200 = 0.26, and 0.26 × 1000 = 260. 52 keeps the old count, 520 multiplies it by 10 instead of 5, and 250 assumes a probability of one fourth without using the data.Show answer and explanation
Relative Frequency: frequently asked questions
How do you calculate relative frequency?
Count how many times the value or event occurs (the frequency), then divide by the total number of observations. If 9 of 36 days were rainy, the relative frequency of rain is 936 = 0.25. Multiply by 100 to write it as a percent, 25%. Check your table: all the relative frequencies should add to 1.
What is the difference between relative frequency and probability?
Relative frequency describes what actually happened in data or an experiment. Theoretical probability describes what should happen in the long run, based on the setup. For a fair coin the probability of heads is 0.5, but 100 flips might give a relative frequency of 0.47. With more and more flips, the relative frequency tends to get closer to 0.5.
Can relative frequency be greater than 1?
No. A category can never occur more times than the total number of observations, so the fraction frequency over total is at most 1, or 100%. It equals 1 only when every observation is in that category, and 0 when none is. A value above 1 means the division was done with the wrong total.
Practice and tools
Sources
- Common Core State Standards, Grade 7 Statistics and Probability (7.SP.C.6)
- Common Core State Standards, Grade 8 Statistics and Probability (8.SP.A.4)
- OpenStax, Introductory Statistics 2e, 1.3 Frequency, Frequency Tables, and Levels of Measurement
Updated November 2026·Reviewed by the Effortless Math team·Standards: CCSS 7.SP.C.6, CCSS 8.SP.A.4
Cite this entry
Effortless Math Team. “Relative Frequency.” Effortless Math Dictionary. Updated November 2026. https://www.effortlessmath.com/math-dictionary/relative-frequency/
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