Relative Frequency Examples in Statistics

Start with the recap, study the fully worked examples, then use the practice problems to check your understanding of Relative Frequency.

This page combines explanation, solved examples, and follow-up practice so you can move from recognition to confident problem-solving in Statistics.

Concept Recap

The fraction or percentage of times a value occurs out of the total number of observations.

Instead of saying '15 students picked pizza,' you say '15 out of 50' or '30%.' Relative frequency compares to the whole, making different-sized groups comparable.

Read the full concept explanation →

How to Use These Examples

  • Read the first worked example with the solution open so the structure is clear.
  • Try the practice problems before revealing each solution.
  • Use the related concepts and background knowledge badges if you feel stuck.

What to Focus On

Core idea: Relative frequency expresses a count as a proportion of the total, enabling fair comparisons between groups of different sizes.

Common stuck point: Students compare raw counts from groups of different sizes and draw incorrect conclusions — always convert to relative frequency before comparing groups.

Worked Examples

Example 1

easy
In a class of 30 students, 12 walk to school, 10 take the bus, 5 cycle, and 3 are driven. Calculate the relative frequency of each transport method.

Solution

  1. 1
    Step 1: Relative frequency = \frac{\text{frequency}}{\text{total}}.
  2. 2
    Step 2: Walk: \frac{12}{30} = 0.4, Bus: \frac{10}{30} \approx 0.333, Cycle: \frac{5}{30} \approx 0.167, Driven: \frac{3}{30} = 0.1.
  3. 3
    Step 3: Check: 0.4 + 0.333 + 0.167 + 0.1 = 1.0 ✓. All relative frequencies sum to 1.

Answer

Walk: 0.40, Bus: 0.33, Cycle: 0.17, Driven: 0.10.
Relative frequency expresses each category's count as a proportion of the total. Unlike raw frequencies, relative frequencies allow comparison between groups of different sizes because they always sum to 1 (or 100%).

Example 2

medium
A die is rolled 200 times with results: 1→30, 2→38, 3→35, 4→32, 5→28, 6→37. Calculate the relative frequency for each outcome and discuss whether the die appears fair.

Practice Problems

Try these problems on your own first, then open the solution to compare your method.

Example 1

medium
School A has 400 students (60 in sports clubs) and School B has 250 students (45 in sports clubs). Which school has a higher proportion of students in sports clubs?

Example 2

hard
A coin is flipped repeatedly. After 10 flips: 7 heads (RF=0.70). After 50 flips: 29 heads (RF=0.58). After 500 flips: 256 heads (RF=0.512). After 5000 flips: 2,520 heads (RF=0.504). Describe the trend and explain what it demonstrates about probability.
← Back to Relative Frequency Practice Mode

Related Concepts

Experimental Probability

Background Knowledge

These ideas may be useful before you work through the harder examples.

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