Distinguish discrete counts from continuous measurements
Classify variables by their possible values · Separate a variable from its recording precision · Choose sensible class intervals for measurements
Exam scope and assessment notes
Core and Extended foundations. Historical study of Cambridge IGCSE Mathematics (US) 0444, 2025 Version 2. The final assessment was June 2025; the syllabus was available only to schools in Arizona, USA. This is not a current exam-entry option. Original self-check teaching and explained practice are not Cambridge papers, official marks or predicted grades. Linked teaching foundations do not establish full syllabus mastery. Calibrated cumulative assessment, reliable drawn-work review and qualified mathematics-teacher review remain unfinished.
Before you begin
- Counting and measurement units
Work on paper. Try each question before revealing help, and explain why your method works.
Quick readiness check
What should you establish before applying the method in this lesson?
What you will learn
- Classify variables by their possible values
- Separate a variable from its recording precision
- Choose sensible class intervals for measurements
Possible values define the type
A discrete variable takes separated possible values, such as a whole-number count of books. A continuous variable can take any value in an interval, such as elapsed time or height. Rounding height to the nearest centimetre makes the recorded numbers integers, but the underlying height variable remains continuous.
A number used as a category label, such as a bus route code, is not a quantitative measurement whose mean has a useful interpretation. Do not classify a variable solely by how its recorded labels look.
Make classes cover without overlap
A grouped time table can use 0≤t<10, 10≤t<20 and 20≤t<30 minutes. A value exactly 10 belongs to the second class. Clear inequalities avoid double-counting boundary observations. State the measurement range and include a suitable additional class if values fall outside the listed range.
Sources for this lesson
Pause and explain
Does rounding a measured time to whole seconds make elapsed time a discrete variable?
Worked example
Is height recorded to the nearest centimetre discrete or continuous?
Show the worked solution
- Height is measured and has possible values between adjacent centimetres.
- Recording precision does not change the underlying variable.
Answer Continuous, with rounded recordings.
Try a topic test
Choose Easy, Normal or Difficult. Save your answers and open worked review after finishing.
Test this topic →From guided practice to a new situation
Write your answer and reasoning first. Use a hint only if you are stuck. The model solution is for self-checking; your written work is not automatically marked.
Classify the number of siblings and the mass of a backpack as discrete or continuous.
Give me a hint
Separate counting from measuring.
Compare my reasoning
- Sibling count takes whole-number values.
- Mass can take intermediate values within a range.
Siblings: discrete; mass: continuous.
Look for these in your work
- Identify possible values
- Use the variable rather than its units alone
Times are grouped as 0≤t<10, 10≤t<20 and 20≤t<30 minutes. Where do 10 and 19.9 belong?
Give me a hint
Check each interval’s included and excluded boundaries.
Compare my reasoning
- 10 is excluded from the first class and included in the second.
- 19.9 also lies in the second class.
Both are in 10≤t<20.
Look for these in your work
- Use non-overlapping boundaries
- Do not round a value into another class
Bus routes have codes 10,20,30. A student calls their mean 20 the average route quality. Evaluate this interpretation.
Give me a hint
The codes identify categories.
Compare my reasoning
- The codes are not quality measurements.
- Changing arbitrary codes would change their numerical mean without changing any quality.
The interpretation is invalid; numerical route labels do not measure quality.
Look for these in your work
- Distinguish category codes from quantities
- Explain why arithmetic is not meaningful here
Common mistakes
- Integer recordings can come from a continuous variable.
- Numerical category codes are not automatically quantities.
What can you explain now?
Does rounding a measured time to whole seconds make elapsed time a discrete variable?
Compare with the explanation
No; the underlying time is continuous.
The measurement can take values between the recorded whole seconds.
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Make it stick
Does rounding a measured time to whole seconds make elapsed time a discrete variable?
If you needed the solution, close it and solve the problem again from a blank page. A correct answer is stronger when you can explain the reason for each step.