Cambridge IGCSE Statistics: Representation of Data — Practice Questions

These are original questions written for Marlbridge, in the style and at the standard of the examination. They are not reproduced past-paper questions — Cambridge holds copyright in its own papers. Use these alongside the official past papers available through your school or Cambridge’s own resources.

Related: Representation of Data study guide and revision notes.

Section A

1. Name the diagram type best suited to keeping every individual data value visible in a small data set. [1]

2. State the vertical axis label required on a histogram with unequal class widths (a Topic 3 skill, tested here for the boundary between topics). [1]

3. Give one advantage and one disadvantage of using a pie chart compared with a bar chart. [2]

Section B

4. A survey of 40 students records their favourite sport (football, cricket, hockey, other) and whether they are in Year 10 or Year 11.

(a) State which type of table is most appropriate for displaying this data, and explain why. [2] (b) Given that 15 Year 10 students chose football and 25 students in total chose football, calculate how many Year 11 students chose football. [2]

5. A class wants to compare the exact reaction times (in milliseconds) of 12 students against the reaction times of another class of 12 students, and wants every individual value from both classes to remain visible on the same diagram.

(a) Name the most appropriate diagram type. [1] (b) Explain why this diagram type is more appropriate here than a grouped bar chart. [2]

6. A survey asks 50 students whether they play a musical instrument and whether they play a sport after school. 18 play both, 12 play only an instrument, 15 play only a sport, and the remainder do neither.

(a) Name the most appropriate diagram for representing this data. [1] (b) Calculate how many students do neither activity. [2]

Section C

7. A school wants to represent the proportion of students choosing each of four elective subjects, and separately wants to compare that proportion between boys and girls.

(a) Explain which single diagram type could show the overall proportion for all students combined. [2] (b) Explain which diagram type would be more appropriate for the boys-versus-girls comparison, and why a single pie chart would not achieve this on its own. [3] (c) Explain one advantage and one disadvantage of your chosen comparison method from part (b). [3]

Worked answers

1. A stem-and-leaf diagram (including back-to-back diagrams for comparing two data sets). [1]

2. Frequency density. [1]

3. Advantage: a pie chart shows proportion of the whole clearly at a glance. Disadvantage: a pie chart is harder than a bar chart to use for comparing exact values between categories. [2]

4. (a) A two-way table is most appropriate, since it cross-tabulates two variables (favourite sport and year group) at once, allowing both individual cell values and row/column totals to be read directly. [2] (b) Total football = 25; Year 10 football = 15; so Year 11 football = 25 - 15 = 10 students. [2]

5. (a) A back-to-back stem-and-leaf diagram. [1] (b) A back-to-back stem-and-leaf diagram keeps every individual reaction time value visible for both classes while still allowing direct visual comparison of their distributions, whereas a grouped bar chart would require grouping the data into class intervals, losing the exact individual values the class wants to keep. [2]

6. (a) A Venn diagram, since the data falls into overlapping categories (playing an instrument and playing a sport are not mutually exclusive). [1] (b) Total = 50. Both = 18, only instrument = 12, only sport = 15. Doing neither = 50 - (18+12+15) = 50 - 45 = 5 students. [2]

7. (a) A single pie chart could show the overall proportion of all students choosing each of the four subjects, since a pie chart represents how a whole (all students) divides into its parts (each subject) as proportional slices. [2] (b) A comparative pie chart (or a sectional/percentage sectional bar chart) would be more appropriate, because a single pie chart can only show one whole (e.g. all students) divided into parts – it cannot show two separate wholes (boys and girls) side by side for direct comparison. A comparative pie chart places two pie charts next to each other, one for each group, allowing a reader to compare the proportional split within each group directly. [3] (c) Advantage: a comparative pie chart lets a reader see both groups’ internal proportional splits at a glance, side by side. Disadvantage: comparing exact values or small differences between the two charts is harder than reading the equivalent values from a table or a sectional bar chart, since visually estimating and comparing two separate pie charts’ slice sizes precisely is less accurate than reading a labelled bar height. [3]

Why this set keeps returning to “which diagram, and why”

Nearly every question in this set asks not just for a diagram to be identified but for a reason connecting the diagram’s properties to the specific data or comparison described, because the revision notes identify Cambridge’s AO2 (10-20% of both papers) as specifically rewarding justification of a chosen method, not just naming it. Question 7 in particular is written to require an explicit “why a single pie chart fails here” argument, since this is exactly the kind of comparative reasoning the revision notes flag as the sub-topic’s most exam-relevant skill.

Official syllabus

Cambridge IGCSE Statistics (0479) syllabus for exams in 2027 – cambridgeinternational.org – the same source cited by the Representation of Data study guide and revision notes.