GCSE Maths Practice: relative-frequency

Question 3 of 10

This question focuses on calculating relative frequency using observed results from repeated trials.

‹ ›

\( \begin{array}{l}\text{A bag contains 4 red, 5 blue, and 6 green marbles.} \\ \text{A marble is drawn 50 times, and a red marble is drawn 15 times.} \\ \text{What is the relative frequency of drawing a red marble?}\end{array} \)

Choose one option:

Relative frequency always uses observed data, not the contents of the bag.

Relative Frequency in GCSE Maths

Relative frequency is an important idea in GCSE Maths probability because it is based on real observations rather than predictions. Instead of calculating how likely something should be using theory, relative frequency looks at what actually happened during an experiment or repeated trial.

What Does Relative Frequency Mean?

Relative frequency tells us how often a particular outcome occurs compared to the total number of times an experiment is carried out. It is found using results that have already been observed. This makes it especially useful in experiments, surveys, and situations where data is collected over time.

The Relative Frequency Formula

The method for calculating relative frequency is always the same:

  • Count how many times the outcome occurred.
  • Divide this by the total number of trials.
  • Simplify the fraction if possible.

Worked Example 1

A spinner is spun 30 times. It lands on yellow 12 times. To find the relative frequency of landing on yellow, divide the number of yellow results by the total number of spins. This gives a fraction that can be simplified.

Worked Example 2

A dice is rolled 40 times. The number 6 appears 10 times. The relative frequency of rolling a 6 is calculated by comparing the number of sixes to the total number of rolls.

Worked Example 3

A student tracks how many days it rains over a 25-day period and records rain on 8 days. The relative frequency of a rainy day is found by dividing the number of rainy days by the total number of days observed.

Common Mistakes

  • Dividing by the wrong total number of trials.
  • Using the number of marbles in the bag instead of the number of draws.
  • Confusing relative frequency with theoretical probability.
  • Forgetting to simplify the fraction.

Why Relative Frequency Is Useful

Relative frequency is widely used in real life. Weather forecasts use past data to estimate future conditions, sports analysts use match statistics to assess performance, and scientists rely on repeated experiments to draw conclusions. In all of these cases, the probability is based on observation rather than theory.

Frequently Asked Questions

Does relative frequency change?
Yes. As more trials are carried out, the relative frequency can change and often becomes more stable.

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 required.

Is relative frequency always accurate?
It is an estimate based on results. Larger numbers of trials usually give more reliable estimates.

Study Tip

If a GCSE question mentions words like observed, recorded, or experiment, it is a strong sign that you should use relative frequency rather than theoretical probability.

Related Quizzes