Choose and interpret a data representation
Build and read frequency and two-way tables, charts and diagrams, then justify which display suits the comparison.
Exam scope and assessment notes
This lesson maps the Choose and interpret a data representation section of Cambridge IGCSE Statistics 0479 (2027 and 2028–2030 syllabus versions). This is original StudyForA teaching and self-check practice, not Cambridge material, an official mark scheme, a timed mock or an official grade. Charts and written working are not automatically assessed; human subject-teacher review remains pending. Use the syllabus version for your exam year. Cambridge offers 0479 in the June series only and does not make it available in every administrative zone. Check the current Cambridge 0479 page and confirm your centre's entry eligibility with your exams officer.
Before you begin
- Use the earlier 0479 ideas where needed; write units, working and a contextual interpretation for each result.
Work on paper. Try each question before revealing help, and explain why your method works.
Quick readiness check
If 18 of 60 learners choose a language, what fraction of the group is that?
What you will learn
- Represent and interpret frequency and two-way tables
- Represent and interpret bar, pie, comparative pie, Venn, box-and-whisker and stem-and-leaf diagrams
- Interpret pictograms without being required to draw them
- Compare the strengths and limits of different representations
Tables organise counts
A frequency table pairs each category or value with its count. In a two-way table, rows and columns classify the same people or objects by two variables; row totals, column totals and the grand total should agree.
Relative frequencies or percentages can compare groups of different sizes, provided each percentage uses the correct group total as its denominator.
Match the display to the data
Bar charts compare category counts; bars are separated because the categories are distinct. Pie charts show parts of one whole, with each sector angle equal to its fraction of the total times 360°. Comparative pie charts use a consistent key and clearly labelled totals so differently sized populations are not confused.
Venn diagrams show overlaps between sets. Box-and-whisker diagrams display the minimum, quartiles, median and maximum, which makes spread and central position easy to compare but hides individual values. Stem-and-leaf diagrams keep the original values visible; back-to-back versions compare two distributions. Pictograms can communicate counts quickly, but the key must be checked carefully.
State what a display can and cannot show
Choose a representation that answers the question. Mention the feature visible in the display and a limitation. A box plot can compare medians and interquartile ranges, for example, but it does not show the shape or exact data values as fully as a stem-and-leaf display.
Pause and explain
A box plot shows a larger interquartile range. What does this support?
Worked example
In a group of 80 students, 30 walk to school and 50 do not. Find the pie-chart angle for those who walk.
Show the worked solution
- The fraction walking is 30/80 = 0.375.
- Multiply by 360°: 0.375 × 360° = 135°.
- Check that the angle is a plausible part of a full 360° circle.
Answer The walking sector is 135°. The other 50 students occupy 225°, and the angles sum to 360°.
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 shows 36 students: 14 take art, 22 do not; 9 of the art students and 8 of the others walk to school. Find the number who do not walk and take art.
Give me a hint
Subtract the art walkers from all art students.
Compare my reasoning
- Art students total 14.
- Art walkers are 9.
- Art students who do not walk = 14 − 9 = 5.
Five students take art and do not walk to school.
Look for these in your work
- Uses the correct row or column total
- Subtracts the matching cell
- States the intersection clearly
A club compares the test scores of two teams with unequal squad sizes. Which display would help compare medians and spread, and what would it hide?
Give me a hint
Think about the five-number summary and whether individual scores remain visible.
Compare my reasoning
- A box-and-whisker diagram displays median and quartiles for each team.
- The same scale is needed for a fair comparison.
- It hides the exact scores and much of the distribution's detailed shape.
A pair of box-and-whisker diagrams on the same scale can compare medians and interquartile ranges. The display does not reveal the individual scores and may hide shape details.
Look for these in your work
- Suitable representation selected
- Common scale mentioned
- Limitation explained
A town has 1200 households, of which 300 recycle weekly. A second town has 800 households, of which 240 recycle weekly. Compare the proportions and recommend a display.
Give me a hint
Convert each count to a percentage before comparing; a paired bar display of percentages is suitable.
Compare my reasoning
- Town A: 300/1200 = 25%.
- Town B: 240/800 = 30%.
- A bar chart of percentages compares the rates without letting the different totals dominate.
Town B has the higher proportion: 30% compared with 25%. A bar chart of the two percentages gives a clear comparison; a chart of raw counts alone would be misleading because the town sizes differ.
Look for these in your work
- Both denominators used
- Comparison correct
- Display choice justified
Common mistakes
- Using bar-chart gaps for continuous grouped intervals
- Comparing raw counts when group totals differ
- Reading a box plot as if it showed the individual observations
- Drawing a pictogram when the syllabus only requires interpretation
What can you explain now?
Which display preserves the individual ordered observations while also showing a distribution's shape?
Compare with the explanation
A stem-and-leaf diagram
Unlike a box plot, a stem-and-leaf display retains the data values.
After trying it yourself, choose your next review. This is your self-assessment.
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Make it stick
Name one display that keeps individual values and one that summarises a distribution using five key values.
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.