GCSE Maths Practice: relative-frequency

Question 2 of 10

This question focuses on calculating relative frequency using data collected from repeated trials.

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\( \begin{array}{l}\text{A bag contains 3 red, 2 blue, and 5 green marbles.} \\ \text{A marble is drawn 50 times, and a red marble is drawn 15 times.} \\ \text{What is the relative frequency of drawing a red marble?}\end{array} \)

Choose one option:

Relative frequency is always based on what actually happened, not what you expect to happen.

Understanding Relative Frequency in GCSE Maths

Relative frequency is a key idea in GCSE Maths probability. It helps us estimate how likely an event is based on what has actually happened during repeated trials, rather than what we expect to happen theoretically. This makes relative frequency especially useful in experiments, surveys, and real-life data collection.

What Is Relative Frequency?

Relative frequency compares how often a specific outcome occurs to the total number of times an experiment is carried out. Instead of predicting results using formulas, we observe outcomes and use those observations to form a probability. The more trials that are carried out, the more reliable the relative frequency usually becomes.

General Method

  1. Identify the outcome you are interested in.
  2. Count how many times this outcome occurred.
  3. Divide this number by the total number of trials.
  4. Simplify the fraction if possible.

Worked Example 1

A spinner is spun 40 times. It lands on blue 18 times. The relative frequency of landing on blue is calculated by dividing 18 by 40. This fraction can then be simplified if possible.

Worked Example 2

A football team wins 9 out of 30 matches in a season. The relative frequency of winning a match is found by dividing the number of wins by the total number of matches played.

Worked Example 3

A student records the number of rainy days over 20 school days and observes rain on 7 days. The relative frequency of a rainy day is found by comparing the number of rainy days to the total number of days observed.

Common Mistakes to Avoid

  • Dividing by the wrong total number of trials.
  • Using the number of possible outcomes instead of observed outcomes.
  • Forgetting to simplify the fraction.
  • Mixing up theoretical probability with relative frequency.

Why Relative Frequency Matters

Relative frequency is widely used in science, sports analysis, weather forecasting, and market research. For example, insurance companies analyse past data to estimate future risk, while sports analysts use match statistics to predict performance trends.

FAQ

Does relative frequency always equal theoretical probability?
Not always. However, as the number of trials increases, relative frequency often gets closer to theoretical probability.

Can relative frequency be written as a decimal or percentage?
Yes. After finding the fraction, it can be converted into a decimal or percentage if needed.

Why do GCSE questions often ask for simplified fractions?
Simplified fractions make probabilities easier to compare and understand.

Study Tip

Whenever you see phrases like "recorded," "observed," or "carried out several times," it is a strong clue that the question is about relative frequency rather than theoretical probability.

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