Relative Frequency Statistics Example 4
Follow the full solution, then compare it with the other examples linked below.
Example 4
hardA 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.
Solution
- 1 Step 1: The relative frequencies approach 0.5 as the number of trials increases: 0.70 → 0.58 → 0.512 → 0.504.
- 2 Step 2: This demonstrates the law of large numbers: as the number of independent trials increases, the relative frequency of an event converges toward its theoretical probability. The early fluctuations (0.70 with 10 flips) stabilise as more data is collected.
Answer
The relative frequency of heads approaches 0.5 as trials increase (0.70 → 0.58 → 0.512 → 0.504). This illustrates the law of large numbers — relative frequency converges to theoretical probability with more trials.
The law of large numbers is a fundamental theorem of probability stating that relative frequency approaches theoretical probability as the number of trials grows. Short-run results can be highly variable, but long-run behaviour is predictable. This is the bridge between theoretical and experimental probability.
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 2 mediumA 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 mediumSchool A has 400 students (60 in sports clubs) and School B has 250 students (45 in sports clubs). W