Relative Frequency Statistics Example 2

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

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.

Solution

  1. 1
    Step 1: Calculate relative frequencies: 1: 30200=0.15\frac{30}{200}=0.15, 2: 38200=0.19\frac{38}{200}=0.19, 3: 35200=0.175\frac{35}{200}=0.175, 4: 32200=0.16\frac{32}{200}=0.16, 5: 28200=0.14\frac{28}{200}=0.14, 6: 37200=0.185\frac{37}{200}=0.185.
  2. 2
    Step 2: For a fair die, each relative frequency should be approximately 16≈0.167\frac{1}{6} \approx 0.167.
  3. 3
    Step 3: All values are between 0.14 and 0.19, which are reasonably close to 0.167 for 200 trials. The die appears approximately fair — the small deviations are consistent with normal random variation.

Answer

Relative frequencies range from 0.14 to 0.19, all close to the theoretical 16≈0.167\frac{1}{6} \approx 0.167. The die appears fair.
Relative frequency provides an empirical estimate of probability. With enough trials, relative frequencies approach theoretical probabilities (law of large numbers). Small deviations from expected values are normal and do not necessarily indicate an unfair die.

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 1 easy

In a class of 30 students, 12 walk to school, 10 take the bus, 5 cycle, and 3 are driven. Calculate

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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