GCSE Maths Practice: relative-frequency

Relative Frequency and Large Numbers of Trials

Relative frequency is a key concept in GCSE Maths probability and becomes especially important when experiments are repeated many times. Unlike theoretical probability, which is based on what should happen in an ideal situation, relative frequency is based on observed results. This makes it a powerful tool for analysing real data.

What Is Relative Frequency?

Relative frequency measures how often a particular outcome occurs compared to the total number of trials. It is always calculated after an experiment has been carried out and relies on recorded observations. As the number of trials increases, the relative frequency often becomes more stable and closer to the theoretical probability.

How to Calculate Relative Frequency

The steps for finding relative frequency are always the same:

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

Worked Example 1

A spinner is spun 150 times. It lands on red 88 times. The relative frequency of landing on red is found by dividing the number of red outcomes by the total number of spins. The resulting fraction can then be simplified.

Worked Example 2

A factory checks 300 products for defects and finds that 27 are faulty. The relative frequency of a defective product is calculated by comparing the number of faulty items to the total number inspected.

Worked Example 3

A weather station records snowfall over 90 days and observes snow on 34 days. The relative frequency of snowfall is found by dividing the number of snowy days by the total number of days recorded.

Common Mistakes to Avoid

• Dividing by the number of possible outcomes instead of the number of trials.
• Using expected probability rather than observed data.
• Leaving fractions unsimplified when simplification is required.
• Confusing relative frequency with theoretical probability.

Why Larger Numbers of Trials Matter

When experiments are repeated many times, the results tend to become more reliable. Small numbers of trials can produce unusual or misleading results, but larger samples usually give a clearer picture of how likely an outcome really is. This idea is important in science, economics, and statistics.

Frequently Asked Questions

Does relative frequency always stay the same?
No. Relative frequency can change as more trials are added, but it usually becomes more stable with larger sample sizes.

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 the question requires it.

Is relative frequency the same as probability?
Relative frequency is an estimate of probability based on observed results, not a guaranteed value.

Study Tip

In GCSE questions, phrases like "repeated many times", "recorded", or "experiment" usually indicate that you should calculate relative frequency rather than theoretical probability.