Cambridge O-Level Statistics: Summary Representation of Data — Practice Questions (4040)

These are original questions written for Marlbridge, in the style and at the standard of the examination. They are not reproduced past-paper questions — examination boards hold copyright in their own papers. Use these alongside the official past papers available free from your board.

Related: Topic 2 study guide

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Section A

1. A survey records 40 students’ favourite subject (Maths, Science, Art) split by gender. State one advantage of organising this data into a two-way table before representing it visually. [2]

2. State two features a stem-and-leaf diagram preserves that a standard bar chart does not. [2]

Section B

3. A dataset of 30 exam scores needs to be represented so both the median and the spread (including any outliers) are clearly visible. Recommend a suitable chart type and justify your choice. [4]

4. A researcher wants to compare the proportion of a school’s budget spent on four categories in two different years. Recommend a suitable chart type and explain one advantage and one disadvantage of your choice. [6]

5. Two dual bar charts show ice-cream sales by flavour for two branches of a shop. Describe two things a candidate could correctly conclude by comparing them. [4]

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Answers

1. A two-way table lets row and column totals be read and compared directly (e.g. total by gender, total by subject) before any chart is drawn, making errors in the raw data easier to spot before they carry through into a visual representation [2].

2. A stem-and-leaf diagram preserves every individual data value (not just grouped totals) [1], and it also shows the shape of the distribution at a glance, similar to a bar chart, while a standard bar chart of grouped data loses the individual values once grouped [1].

3. A box-and-whisker diagram is most suitable [1], because it directly displays the median as the central line of the box [1], shows the spread of the middle 50% of the data via the interquartile range (the box width) [1], and clearly marks any outliers separately from the whiskers, which a simple bar chart or pie chart cannot show [1].

4. A comparative pie chart (two pie charts, one per year) is suitable [1], since a pie chart’s main advantage is showing each category’s proportion of the whole clearly at a glance [1] [1]. The main disadvantage is that comparing exact values between the two years is harder than with a bar chart, since angle/area comparisons are less precise than reading bar heights against a scale [1] [1].

5. Any two of: which flavour sold best at each branch individually [1] [1]; which branch had higher total sales for a specific flavour when comparing the two charts directly [1] [1]; whether the pattern of best/worst-selling flavours is the same or different between the two branches [1] [1] (maximum 4 marks for two valid, chart-based comparisons).

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Exam technique for this topic

Every question in this topic ultimately tests one of three skills: constructing a representation correctly, choosing the right representation and justifying that choice, or interpreting a representation already given. Treat these as three separate skills to practise individually rather than assuming fluency in one implies fluency in the others — a candidate who can draw a box-and-whisker diagram perfectly may still lose marks on a question asking them to justify why it, rather than a bar chart, suits a given dataset. When justifying a chart choice, always name the specific feature of the data (proportions of a whole, individual values needing preservation, spread and outliers) that makes your chosen chart the right fit, since a generic “it’s clear and easy to read” answer earns no marks — examiners are testing matched judgement, not general chart appreciation.

Building this topic’s skills incrementally

Because this topic asks candidates to construct, choose and interpret representations as three distinct skills, revision is most effective when each skill is drilled in isolation before combining them. Start by drawing every named chart type from the same simple raw dataset, so the differences in what each chart preserves and obscures become obvious side by side. Then practise the choose-the-right-chart skill separately, using short scenario prompts (a proportion-of-a-whole dataset, a dataset needing individual values preserved, a dataset needing spread and outliers shown) and forcing yourself to name the specific feature of each scenario that determines the answer. Only once both of those are secure does it make sense to practise the interpretation skill on completed charts and tables, since interpretation depends on already knowing what each chart type is naturally suited to showing.

Practising with real classroom data

Building your own small dataset — for example, recording the time each classmate takes to complete a short task, or the number of books read by each student in a month — and then representing it with several different chart types side by side is one of the most effective ways to internalise this topic, since seeing the same real numbers rendered as a bar chart, a box-and-whisker diagram and a stem-and-leaf diagram at once makes the differences between what each chart preserves immediately concrete, rather than abstract textbook knowledge.

Where marks are usually lost

• Recommending a chart type without justifying the choice against a specific feature of the dataset described.
• Constructing a stem-and-leaf diagram with an unordered leaf row, which loses marks even when the underlying values are correct.
• Describing a chart’s appearance (“the bars are different heights”) instead of stating a data-based conclusion.
• Confusing a pie chart’s strength (showing proportion) with a bar chart’s strength (showing exact comparative values).
• Reading a two-way table’s row and column totals inaccurately under time pressure, which then produces an incorrect chart or conclusion built on that misread figure.
• Answering an interpretation question (like Q5) with a single vague observation rather than two clearly separate, chart-grounded comparisons.