Relative Frequency Statistics Example 1

Follow the full solution, then compare it with the other examples linked below.

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 = frequencytotal\frac{\text{frequency}}{\text{total}}.
  2. 2
    Step 2: Walk: 1230=0.4\frac{12}{30} = 0.4, Bus: 1030≈0.333\frac{10}{30} \approx 0.333, Cycle: 530≈0.167\frac{5}{30} \approx 0.167, Driven: 330=0.1\frac{3}{30} = 0.1.
  3. 3
    Step 3: Check: 0.4+0.333+0.167+0.1=1.00.4 + 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%).

About Relative Frequency

Relative frequency is the fraction or percentage of times a value occurs out of the total number of observations. It converts raw counts into proportions, enabling fair comparisons between groups of different sizes.

Learn more about Relative Frequency →

More Relative Frequency Examples

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 f

Example 3 medium

School A has 400 students (60 in sports clubs) and School B has 250 students (45 in sports clubs). W

Example 4 hard

A coin is flipped repeatedly. After 10 flips: 7 heads (RF=0.70). After 50 flips: 29 heads (RF=0.58).

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