Discrete and Continuous Data
Master Discrete and Continuous Data for GCSE Statistics with this free worksheet and full mark scheme — Foundation and Higher exam-style questions with worked answers for AQA and Edexcel. Discrete data take only certain values (usually counted), while continuous data can take any value in a range (measured).
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These worksheets and mark schemes are original, written for Virtus Academy and checked against the current AQA and Edexcel specifications. Every worksheet comes with a full mark scheme.
Topic overview
Quantitative data divides into discrete and continuous, and the distinction determines which diagrams and class intervals are appropriate.
Discrete data can only take certain separate values, usually whole numbers obtained by counting. The number of siblings, the number of cars passing, and shoe sizes are all discrete.
Continuous data can take any value within a range and is obtained by measuring. Height, mass, time and temperature are all continuous. The practical consequence is that continuous data must be grouped into class intervals with no gaps, written using inequalities such as \(150 \leq h < 160\), whereas discrete data can use gaps such as 1–5 and 6–10.
Revision notes
Discrete data
Data that can only take certain separate values, usually whole numbers obtained by counting.
Examples: number of siblings, number of goals scored, shoe size. There are gaps between possible values — you cannot have 2.5 siblings.
Continuous data
Data that can take any value within a range, obtained by measuring.
Examples: height, mass, time, temperature. Between any two values there is always another possible value, limited only by the precision of the measuring instrument.
Class intervals
Continuous data must be grouped with no gaps, using inequalities such as \(150 \leq h < 160\) and \(160 \leq h < 170\).
Discrete data can use intervals with gaps, such as 1–5 and 6–10, because no value falls between 5 and 6.
Key points
- Discrete data takes separate values only.
- Discrete data comes from counting.
- Continuous data takes any value in a range.
- Continuous data comes from measuring.
- Continuous class intervals must have no gaps.
- Inequalities are used for continuous intervals.
Worked examples
Example 1
State whether the time taken to run 100 m is discrete or continuous. [1 mark]
Working
Example 2
Explain why class intervals for continuous data must not have gaps. [2 marks]
Working
Example 3
A student records shoe sizes. State the type of data and explain your answer. [2 marks]
Working
Common mistakes
Calling age continuous when recorded in whole years.
Age is continuous, though it is often recorded discretely — read the question carefully.
Using gaps in continuous class intervals.
Use inequalities so every possible value has an interval.
Saying discrete data cannot be decimals.
Shoe sizes include halves but are still discrete, because values between are impossible.
Confusing counting and measuring.
Counting gives discrete data; measuring gives continuous data.
Exam tips
- Ask whether the data was counted or measured.
- Use inequalities for continuous class intervals.
- Check that intervals cover every possible value.
- Remember discrete values have gaps between them.
Key terms
- Discrete
- Data taking only certain separate values.
- Continuous
- Data taking any value within a range.
- Class interval
- A group into which data is placed.
- Inequality
- A symbol such as \(\leq\) used to define continuous intervals.
Related topics
Written and reviewed against the current AQA and Edexcel specifications. Spotted an error? Let us know.