IGCSE Mathematics: Statistics — 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 — examination boards hold copyright in their own papers. Use these alongside the official past papers available free from your board.

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Questions

1. State whether each of these is discrete or continuous data: (a) the number of siblings each student in a class has; (b) the height of each student in a class. [2]

2. A survey records the number of pets owned by 30 households, presented as a bar chart. Explain one advantage and one disadvantage of presenting this data as a bar chart rather than as a simple list. [2]

3. The number of goals scored by a football team in 6 matches is: 4, 7, 7, 9, 12, 15.

(a) Calculate the mean. [2] (b) Find the median. [1] (c) State the mode. [1] (d) Calculate the range. [1]

4. A pie chart is used to show how 120 students travel to school. The “walk” sector has an angle of 90°. Calculate the number of students who walk to school. [2]

5. A scatter diagram plots students’ scores in a maths test against their scores in a science test, showing a positive correlation.

(a) State what “positive correlation” means in this context. [1] (b) A line of best fit is drawn. Explain how it could be used to estimate a science score for a student who scored 65 in the maths test but was absent for the science test. [1]

6. (Extended) The table shows the ages of 50 people at an event.

Age (years)	0–10	10–20	20–30	30–40	40–50
Frequency	4	10	16	14	6

(a) Calculate the cumulative frequency for each class, and state the cumulative frequency for “age < 30”. [2] (b) Use interpolation within the class to estimate the median age. [2]

7. (Extended) In a histogram, one bar represents a class with width 5 and frequency 15. Calculate the frequency density for this bar. [2]

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Answers

1. (a) Discrete — it can only take whole-number values [1]. (b) Continuous — it can take any value within a range [1].

2. Advantage: a bar chart makes the overall pattern easy to see at a glance [1]. Disadvantage: exact individual values can be harder to read precisely than from a list, especially between grid lines [1]. (Any other valid, opposite pair of points should be credited.)

3. (a) Mean = (4 + 7 + 7 + 9 + 12 + 15) ÷ 6 = 54 ÷ 6 [1] = 9 [1]. (b) Ordered: 4, 7, 7, 9, 12, 15 — the middle two values are 7 and 9, so median = (7 + 9) ÷ 2 = 8 [1]. (c) 7 — it appears most often [1]. (d) Range = 15 − 4 = 11 [1].

4. Fraction walking = 90° ÷ 360° = ¼ [1]. Number walking = ¼ × 120 = 30 students [1].

5. (a) As one variable increases, the other also tends to increase [1]. (b) Find 65 on the maths-score axis, go up to the line of best fit, then across to the science-score axis to read off the estimated science score [1].

6. (a) Cumulative frequencies: 4, 14, 30, 44, 50 [1]. Cumulative frequency for age < 30 is 30 [1]. (b) The median is the 25th value (of 50). This falls in the 20–30 class, where the cumulative frequency reaches 14 at age 20 and 30 at age 30 [1]. Estimated median = 20 + ((25 − 14) ÷ 16) × 10 = 20 + 6.9 = 26.9 years (3 s.f.) [1].

7. Frequency density = frequency ÷ class width = 15 ÷ 5 = 3 [2].

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Where marks are usually lost

• Calling data “discrete” or “continuous” based on how it is displayed rather than what it actually measures — a count is always discrete, a measurement is always continuous, whatever the scale used.
• Forgetting to order the data before finding the median, or taking the middle position number as the median instead of the value at that position.
• Confusing mode (most frequent value) with median (middle value) and mean (average) — all three are asked for separately and are rarely equal.
• In a pie chart question, using the angle as if it were the answer itself, rather than converting the angle to a fraction of 360° first.
• Describing correlation as “one causes the other” — correlation only describes a pattern in the data, not a cause-and-effect relationship.
• On a histogram, plotting frequency directly on the y-axis instead of frequency density (frequency ÷ class width) — a histogram’s vertical axis is frequency density whether or not the class widths happen to be equal, which is what makes a histogram meaningfully different from a categorical bar chart. The distinction becomes especially important, and the two axes give visibly different-shaped bars, once the class widths are unequal.

Examiner report insight

• When reading a value (e.g. the median) from a stem-and-leaf diagram, record the full value – stem and leaf together – not just the leaf digit found in the middle row.
• If a question adds a constant to every data value, update both the mode and the median by that constant, not just one of them (the range stays unchanged either way).
• When reading an interquartile range from a cumulative frequency graph, record both quartile readings as working before subtracting – giving only the final difference, with no readings shown, risks losing the method mark even with a correct final answer.

Source: Cambridge International, 0580 Mathematics Principal Examiner Report, June 2024 series, Papers 12, 22, 23, 31 (verified 2026-09-02).