EDEXCEL GCSE FOUNDATION MATHS - What is Relative Frequency

Edexcel GCSE Foundation Maths: Understanding Relative Frequency

What is Relative Frequency?

Relative frequency is a way of measuring how often something happens in a set of data. It's expressed as a fraction, decimal or percentage.

How to calculate Relative Frequency:

1. Identify the event: The specific outcome you're interested in.
2. Count the occurrences: How many times does this event happen in your data set?
3. Divide by the total: Divide the number of occurrences by the total number of trials or observations.

Formula:

Relative Frequency = (Number of occurrences of the event) / (Total number of trials)

Example:

Let's say you roll a dice 20 times and get the following results:

• 1: 3 times
• 2: 4 times
• 3: 2 times
• 4: 5 times
• 5: 3 times
• 6: 3 times

Calculate the relative frequency of rolling a 4:

1. Event: Rolling a 4.
2. Occurrences: The number 4 appears 5 times.
3. Total trials: You rolled the dice 20 times.

Relative Frequency: (5/20) = 0.25 or 25%

Interpreting Relative Frequency:

The relative frequency of 0.25 means that in this experiment, a 4 was rolled 25% of the time.

Why is Relative Frequency Important?

• Predicting future outcomes: Relative frequency helps estimate the likelihood of an event happening in the future.
• Comparing probabilities: It allows you to compare the likelihood of different events happening.
• Understanding trends: By analysing relative frequencies over time, you can identify patterns and trends in data.

Key Points:

• Relative frequency is always a number between 0 and 1.
• A relative frequency of 0 means the event never happened, while a relative frequency of 1 means it happened every time.
• As the number of trials increases, the relative frequency usually gets closer to the true probability of the event.

Practice Problems:

1. A coin is flipped 50 times, and heads appears 28 times. Calculate the relative frequency of getting heads.
2. In a class of 30 students, 18 students like chocolate, 12 like strawberry, and 5 like both. Calculate the relative frequency of students who like only chocolate.

By understanding relative frequency, you gain a valuable tool for interpreting data and making informed predictions.