GCSE Maths Practice: relative-frequency

Relative Frequency in Experimental Probability

Relative frequency is a central concept in GCSE Maths probability, particularly at Higher tier. It is used to describe how often an outcome occurs based on real experimental data rather than theoretical assumptions. This allows us to analyse results from experiments such as spinner trials, dice rolls, and surveys.

Understanding Relative Frequency

Relative frequency compares the number of times an event occurs to the total number of trials carried out. Because it is based on observations, the value may vary each time an experiment is repeated. However, when the number of trials is large, relative frequency usually gives a more reliable picture of how likely an outcome is.

General Method

The process for calculating relative frequency is always the same:

• Identify the outcome you are interested in.
• Count how many times this outcome occurred.
• Divide this number by the total number of trials.
• Simplify the fraction or convert it to a decimal if required.

Worked Example 1

A spinner is spun 150 times and lands on blue 37 times. The relative frequency of landing on blue is calculated by dividing the number of blue outcomes by the total number of spins. The answer can then be simplified or written as a decimal.

Worked Example 2

A dice is rolled 200 times and an even number appears 91 times. The relative frequency of rolling an even number is found by comparing the number of even outcomes to the total number of rolls.

Worked Example 3

A student records how often they revise over a 40-day period and notes revising on 17 days. The relative frequency of revising is calculated by dividing the number of revision days by the total days recorded.

Common Higher-Tier Errors

• Dividing by the number of sections on the spinner instead of the number of spins.
• Using theoretical probability instead of experimental data.
• Failing to simplify fractions fully.
• Rounding too early and reducing accuracy.

Why Relative Frequency Is Useful

Relative frequency is widely used to analyse real-world data. Scientists use it to interpret experimental results, businesses use it to identify customer trends, and sports analysts use it to assess performance. In each case, conclusions are based on observed evidence rather than assumptions.

Fractions and Decimals at Higher Tier

At Higher GCSE level, you may be expected to express relative frequency as a simplified fraction or a decimal, depending on how the answers are presented. Always check the format of the answer choices before deciding how to present your final answer.

Frequently Asked Questions

Can relative frequency change if the experiment is repeated?
Yes. Different runs of the same experiment can produce different results due to random variation.

Is relative frequency the same as probability?
Relative frequency is an estimate of probability based on observed data.

Does a larger number of trials matter?
Yes. Larger samples usually give more reliable estimates.

Study Tip

In Higher GCSE probability questions, always focus on the data given. If the question describes an experiment, relative frequency should be calculated using the observed results, not theoretical probability.