Classifying data and two-way tables
Distinguish categories, discrete counts and continuous measurements, then organise observations without overlap.
Core and Extended.
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.