Organise, classify and interpret data
Classify data, build frequency and two-way tables, compare groups and make conclusions that respect the sample's limits.
Use this pathway for Cambridge IGCSE International Mathematics 0607, 2028–2030. Core and Extended objectives are labelled in each lesson; Extended adds requirements beyond Core. Paper 1 and Paper 2 are non-calculator. Papers 3–6 require a graphic display calculator (GDC). These original lessons use self-checked practice; they are not a Cambridge grade, full timed paper or teacher review.
Before you begin
- Check whether your school has entered you for Core or Extended. Core and Extended share most Number ideas, but some notation and methods are Extended only.
Work on paper. Try each question before revealing help, and explain why your method works.
Quick readiness check
Which type of data records a measured quantity that can vary continuously?
What you will learn
- Distinguish categorical, discrete and continuous data
- Organise counts in tally and two-way tables
- Interpret comparisons without claiming more than the data show
Classify before choosing a table
Categorical data name groups; discrete data are countable values; continuous data are measured and can take any value in an interval. A tally table records counts, and a two-way table organises two categorical variables.
Check that row totals, column totals and the grand total agree. For a conditional comparison, use the correct group total as the denominator rather than comparing raw counts from groups of different sizes.
Describe what the evidence supports
Read labels, units, scales and sample sizes before comparing. A larger average or frequency in one sample does not by itself prove the same pattern holds in the whole population or establish a cause.
State a conclusion with its evidence and limitation. Data from a self-selected or small sample may not represent a wider group.
Pause and explain
Why compare proportions rather than raw counts for groups of different sizes?
Worked example
A survey records 18 of 30 Year 10 students and 12 of 24 Year 11 students choosing Biology. Compare the proportions.
Show the worked solution
- Year 10 proportion = 18/30 = 0.6.
- Year 11 proportion = 12/24 = 0.5.
- In these samples the Year 10 proportion is 0.1 higher; the result alone does not establish why or generalise to all students.
Answer Year 10: 60%; Year 11: 50%; the sampled Year 10 proportion is 10 percentage points higher.
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.
A two-way table has 20 students: 9 study French, 7 study Korean and 4 study both. How many study neither, and what proportion study at least one?
Give me a hint
Use inclusion-exclusion for the union, then compare with 20.
Compare my reasoning
- At least one = 9 + 7 − 4 = 12.
- Neither = 20 − 12 = 8.
- Proportion studying at least one = 12/20 = 0.6.
8 study neither; 60% study at least one.
Look for these in your work
- Overlap subtracted once
- Neither found from total
- Proportion simplified
Classify each variable: shoe size, time to run 100 m, and favourite subject.
Give me a hint
Ask whether the value is a count/ordered step, a measurement, or a label.
Compare my reasoning
- Shoe size is discrete: values come in set increments.
- Run time is continuous: it is measured and can include decimal values.
- Favourite subject is categorical: it is a label.
Shoe size: discrete; run time: continuous; favourite subject: categorical.
Look for these in your work
- Discrete distinguished from continuous
- Measurement identified
- Category identified
A voluntary online poll shows 72% of 50 respondents prefer a new timetable. Give one valid conclusion and one limitation.
Give me a hint
Separate what the sample directly shows from whether it represents a broader group.
Compare my reasoning
- In the poll, about 72% of respondents preferred the timetable.
- Only 50 people responded, and volunteers may differ from non-respondents.
- The poll cannot alone establish the view of every student or the reason for preferences.
72% of these respondents preferred it; a small voluntary sample may not represent all students.
Look for these in your work
- Sample-based statement made
- Sampling limitation identified
- Overclaim avoided
Common mistakes
- Comparing counts when group sizes differ
- Mixing up discrete and continuous variables
- Ignoring missing or self-selected responses
- Claiming a cause from a descriptive comparison
What can you explain now?
Is the number of books borrowed a discrete or continuous variable?
Compare with the explanation
Discrete
It is a count of whole books.
After trying it yourself, choose your next review. This is your self-assessment.
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Make it stick
What should you check before comparing two data sets or generalising a survey result?
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.