Averages & Spread - AQA GCSE Mathematics Revision

Topic overview

What you need to know

Averages & Spread is a key part of GCSE Mathematics. Build fluency with the method, then apply it to unfamiliar and multi-step problems. The sum of all values divided by the number of values. Mean = Σx ÷ n. The middle value when data is arranged in order. For n values, the median is the (n+1)/2 th value. The value that appears most frequently in a data set. There can be more than one mode.

Exam tip

Write every stage of your method. Method marks can still be earned when the final answer is wrong.

Revision notes

Core ideas

Secure these ideas first. Say each definition in your own words, then connect it to the topic overview.

Mean: The sum of all values divided by the number of values. Mean = Σx ÷ n.
Median: The middle value when data is arranged in order. For n values, the median is the (n+1)/2 th value.
Mode: The value that appears most frequently in a data set. There can be more than one mode.
Range: The difference between the largest and smallest values: range = max − min.

Revision notes

Apply it in the exam

The exam will rarely ask for an isolated definition. Practise selecting the right idea and using it as part of a complete explanation or method.

Interquartile Range (IQR): IQR = Q3 − Q1. The range of the middle 50% of the data. Less affected by outliers.
Quartiles: Q1 (lower quartile) = 25th percentile, Q2 (median) = 50th percentile, Q3 (upper quartile) = 75th percentile.
Estimated Mean from a Frequency Table: Use midpoints of each class. Estimated mean = Σ(midpoint × frequency) ÷ Σfrequency.
Outlier: An extreme value that lies far from the rest of the data. Often defined as more than 1.5 × IQR from the quartiles.

Core knowledge

Key facts for Averages & Spread

8 essentials

Mean

The sum of all values divided by the number of values. Mean = Σx ÷ n.

Median

The middle value when data is arranged in order. For n values, the median is the (n+1)/2 th value.

Mode

The value that appears most frequently in a data set. There can be more than one mode.

Range

The difference between the largest and smallest values: range = max − min.

Interquartile Range (IQR)

IQR = Q3 − Q1. The range of the middle 50% of the data. Less affected by outliers.

Quartiles

Q1 (lower quartile) = 25th percentile, Q2 (median) = 50th percentile, Q3 (upper quartile) = 75th percentile.

Estimated Mean from a Frequency Table

Use midpoints of each class. Estimated mean = Σ(midpoint × frequency) ÷ Σfrequency.

Outlier

An extreme value that lies far from the rest of the data. Often defined as more than 1.5 × IQR from the quartiles.

Active recall

Close the notes and answer these

1.Without looking, explain mean and give one example or consequence.
2.Without looking, explain median and give one example or consequence.
3.Without looking, explain mode and give one example or consequence.
4.Without looking, explain range and give one example or consequence.

Content reviewed 23 July 2026 against the current linked specification.

Finished learning?

Mark the notes complete, then test what you can recall.

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