Key takeaway: Relative frequency is the fraction of all the data that falls in one category, found by dividing that category’s count by the total number of data values.
Grade 88.SP.A.4Statistics and Data
Definition of Relative Frequency
Relative frequency says how big a category is compared with the whole. A raw count of 18 means little by itself: 18 out of 20 is nearly everyone, while 18 out of 200 is a small group.
To get it, divide the category count, called its frequency, by the total number of observations. You may write the result as a fraction, a decimal or a percent. All of them in one data set add up to 1, or 100%, and they allow fair comparisons between groups of different sizes, for example two classes with different enrollments.
Formula and notation
For a category with frequency \(f\) in a data set of \(n\) values:
\[\text{relative frequency} = \frac{f}{n}\]
Multiply by 100 to express it as a percent. In a two-way table, \(n\) can be a row total or a column total, depending on which group the question asks about.
Key facts
- Every relative frequency is between 0 and 1, or between 0% and 100%.
- The relative frequencies of all categories in one data set total exactly 1.
- It compares groups of different sizes on a fair, equal footing.
- Experimental probability is this same ratio for outcomes in trials.
Relative Frequency example
A cafeteria asks 50 students for their favorite lunch: 18 pick pizza, 14 tacos, 10 burgers and 8 salad. Find the relative frequency of each choice as a percent.
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Pizza: \(\frac{18}{50} = 0.36 = 36\%\). Tacos: \(\frac{14}{50} = 0.28 = 28\%\).
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Burgers: \(\frac{10}{50} = 0.20 = 20\%\). Salad: \(\frac{8}{50} = 0.16 = 16\%\).
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Check the total: \(36 + 28 + 20 + 16 = 100\%\).
The relative frequencies are 36%, 28%, 20% and 16%.
Common mistake
Watch out
Zoe divides the pizza count by the number of categories: \(18 : 4 = 4.5\), and reports a relative frequency of 4.5.
Why it is wrong
The divisor must be the total number of responses, 50, not the number of categories. A relative frequency can never exceed 1, so 4.5 signals an error. The correct value is \(\frac{18}{50} = 0.36\).
Related terms and lessons
Browse the glossary: A–Z list · Grade 8 vocabulary · Statistics and Data