Classifying data and two-way tables
Distinguish categories, discrete counts and continuous measurements, then organise observations without overlap.
Core and Extended. This is the separate 9–1 qualification 0980. Cambridge intends Core for grades 4–1 and Extended for grades 9–5; the eligible award bands are grades 5–1 for the Core papers and grades 9–3 for the Extended papers.
Before you begin
- Add whole-number frequencies.
- Read row and column headings.
Work on paper. Try each question before revealing help, and explain why your method works.
Quick readiness check
Which is a continuous variable?
What you will learn
- Classify numerical and categorical data.
- Complete tally, frequency and two-way tables.
Choose categories that match the observations
Favourite subject is categorical; number of siblings is a discrete count; height is a continuous measurement even when recorded to the nearest centimetre. Continuous variables can take any value in a range, while counts use separate possible values. Recording precision does not change the underlying type.
A tally records each observation once, often in groups of five for easier checking. Frequencies count the tallies. Categories should be exhaustive and non-overlapping: every observation fits one category. For grouped heights, intervals such as 150 ≤ h < 160 and 160 ≤ h < 170 avoid placing a boundary value in two groups.
Two-way tables cross-classify the same group
A table can classify twenty learners by year group and travel method. If Year 7 has six bus and four walk, and Year 8 has three bus and seven walk, the row totals are ten each. The bus column totals nine and the walk column eleven; both routes to the grand total give twenty.
Use subtraction to fill a missing cell from its row or column total, then check the other total. A table of the same people does not contain independent new samples in each row. Label units and categories so a reader knows whether a cell counts people, percentages or measurements.
Pause and explain
A row total is 18; one of its two cells is 7. Find the other cell.
Worked example
Year 7: bus 6, walk 4. Year 8: bus 3, walk 7. Find travel totals and grand total.
Show the worked solution
- Bus total is 6 + 3 = 9.
- Walk total is 4 + 7 = 11.
- Nine plus eleven gives twenty, agreeing with the two row totals of ten.
Answer Bus 9, walk 11; total 20.
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 favourite colour, number of pets and mass.
Give me a hint
Separate categories, counts and measurements.
Compare my reasoning
- Favourite colour is categorical.
- Number of pets is discrete numerical data.
- Mass is continuous numerical data.
Categorical; discrete; continuous.
Look for these in your work
- Used the underlying variable.
- Separated counts from measurements.
A two-way table has first row 8,5 and second row 4,9. Find row totals, column totals and total.
Give me a hint
Check the grand total in both directions.
Compare my reasoning
- Row totals are thirteen and thirteen.
- Column totals are twelve and fourteen.
- Both sums give twenty-six.
Rows 13,13; columns 12,14; total 26.
Look for these in your work
- Added matching cells.
- Checked consistent totals.
Why are 10 ≤ x ≤ 20 and 20 ≤ x ≤ 30 unsuitable as adjoining groups?
Give me a hint
Test the boundary value twenty.
Compare my reasoning
- Twenty satisfies both intervals.
- An observation could be counted twice.
- Use 10 ≤ x < 20 and 20 ≤ x < 30, with a suitable final endpoint.
They overlap at 20; use non-overlapping boundaries.
Look for these in your work
- Identified the shared boundary.
- Repaired the intervals.
Common mistakes
- Overlapping group boundaries.
- Confusing a recorded rounded measurement with a count.
- Leaving table totals unchecked.
What can you explain now?
Does rounding a measured height make the underlying variable discrete?
Compare with the explanation
No.
The measurement is continuous; its recorded precision is a separate matter.
After trying it yourself, choose your next review. This is your self-assessment.
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Make it stick
Tomorrow, classify three variables and complete a small two-way table in both directions.
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.