These are original Marlbridge practice questions, not past exam questions. All data sets are fictional. The rubrics are a suggested Marlbridge rubric to help you check your work; they are not an official scoring guideline. Assumptions for every question: each individual gives exactly one answer unless the question says otherwise; slice angle = relative frequency × 360°; give proportions to 2 decimal places and angles to 1 decimal place unless they are exact. A four-function calculator is enough.
Question 1 (multiple choice · foundation)
A fictional chess club asked its 72 members which day they prefer for meetings. In the pie chart of the results, the Thursday slice has an angle of 100°. How many members prefer Thursday?
- (A) 20
- (B) 27.8
- (C) 72
- (D) 100
Answer and explanation
Answer: (A). The slice is 100 ÷ 360 of the circle, so the relative frequency is 0.2777… . The count is (100 ÷ 360) × 72 = 20 members.
- (B) is the percentage of members (27.8%), not the number of members. A count must also be a whole number.
- (C) treats the 100° as if it were 100%, which would mean every member chose Thursday. A whole circle is 360°, not 100°.
- (D) reads the angle as a count. The angle only shows a share of the whole.
Question 2 (multiple choice · core)
A fictional shop asked 100 shoppers to choose between two brands of orange juice: 48 chose Brand A and 52 chose Brand B. An advert shows a bar chart of the counts in which the vertical axis starts at 45, not 0. Which statement is correct?
- (A) Brand B was chosen by more than twice as many shoppers as Brand A, as the bars show.
- (B) Brand B was chosen by 4 more shoppers than Brand A; the bars exaggerate the difference because the axis does not start at 0.
- (C) The chart is misleading, so it is impossible to tell which brand was chosen by more shoppers.
- (D) A correct pie chart of these data would show Brand B’s slice more than twice the size of Brand A’s.
Answer and explanation
Answer: (B). Measured from 45, the bars are 48 − 45 = 3 and 52 − 45 = 7 units tall, so B’s bar looks 7 ÷ 3 ≈ 2.33 times as tall as A’s. The real ratio is 52 ÷ 48 ≈ 1.08: B was chosen by 4 more shoppers, about 8% more than A.
- (A) trusts the visible bar heights. With a truncated axis the heights are not in proportion to the counts.
- (C) goes too far. The values are still readable from the axis: 52 > 48, so B was chosen by more shoppers. Only the visual size is misleading.
- (D) is wrong because a pie chart’s slices are in proportion to the counts: 52 ÷ 100 × 360° = 187.2° and 48 ÷ 100 × 360° = 172.8°, a ratio of about 1.08.
Question 3 (multiple choice · core)
Two fictional schools recorded what each student did for lunch on one day.
| Lunch | School P (n = 150) | School Q (n = 80) |
|---|---|---|
| Hot meal | 60 | 40 |
| Packed lunch | 75 | 28 |
| No lunch | 15 | 12 |
Which claim do these data support?
- (A) A hot meal is more popular at School P, because 60 students there chose one against 40 at School Q.
- (B) A larger proportion of students at School Q than at School P chose a hot meal.
- (C) Half of the students at School Q brought a packed lunch.
- (D) At both schools, a majority of students chose a hot meal.
Answer and explanation
Answer: (B). Hot meal: School P 60 ÷ 150 = 0.40; School Q 40 ÷ 80 = 0.50. So 50% of School Q students chose a hot meal against 40% at School P.
- (A) compares counts from groups of different sizes. School P has nearly twice as many students, so its counts are larger in general; the proportions show the opposite.
- (C) mixes up the schools. Half of School P (75 ÷ 150 = 0.50) brought a packed lunch; at School Q it was 28 ÷ 80 = 0.35.
- (D) fails at both schools: 0.40 is not a majority, and 0.50 is exactly half, not more than half.
Question 4 (calculation · core)
A fictional animal shelter recorded the type of every animal adopted last month: Dog 27, Cat 21, Rabbit 6, Other 6.
(a) Calculate the relative frequency of each type. (b) Calculate the slice angle of each type for a pie chart, and check your angles. (c) Describe how to draw a relative frequency bar chart of these data.
Worked solution
(a) n = 27 + 21 + 6 + 6 = 60. Dog 27 ÷ 60 = 0.45; Cat 21 ÷ 60 = 0.35; Rabbit 6 ÷ 60 = 0.10; Other 6 ÷ 60 = 0.10. Check: 0.45 + 0.35 + 0.10 + 0.10 = 1.00.
(b) Dog 0.45 × 360° = 162°; Cat 0.35 × 360° = 126°; Rabbit 0.10 × 360° = 36°; Other 36°. Check: 162 + 126 + 36 + 36 = 360°.
(c) Four separate bars of equal width with gaps between them, labelled Dog, Cat, Rabbit and Other on the horizontal axis (largest first). Vertical axis labelled “Relative frequency”, starting at 0 with an even scale, for example 0 to 0.50 in steps of 0.10. Bar heights 0.45, 0.35, 0.10 and 0.10. A title such as “Animals adopted last month (n = 60)”.
Suggested mark points (3): 1 for all four relative frequencies with n = 60 shown; 1 for all four angles and a check that they total 360°; 1 for a bar chart description with separate equal-width bars, a labelled axis that starts at 0 and the correct heights. Angles found as 45°, 35°, 10° and 10° (percentages used as degrees) earn no credit for (b).
Question 5 (constructed response · core)
A fictional town council asked 240 residents which one new facility they would most like. The bar chart shows the results.
(a) How many residents chose the swimming pool, and how many chose the library? (b) A councillor says: “Most residents want a swimming pool.” Is this claim supported? Explain. (c) A second councillor says: “Fewer than 1 in 5 residents chose the cinema.” Is this claim supported? Explain.
Worked solution and suggested Marlbridge rubric
(a) Swimming pool: 0.35 × 240 = 84 residents. Library: 0.25 × 240 = 60 residents.
(b) Not supported. The swimming pool is the most common choice (0.35, the tallest bar), but “most residents” means more than half. Only 35% chose it, so 1 − 0.35 = 0.65 of the residents (156 of the 240) chose something else. A fair statement is: “The swimming pool was the most popular single choice, chosen by 35% of the 240 residents surveyed.”
(c) Not supported. 1 in 5 is 0.20. The cinema bar reaches exactly 0.20, so exactly 1 in 5 residents (0.20 × 240 = 48) chose the cinema, not fewer than 1 in 5.
| Point | What earns it |
|---|---|
| 1 | Both counts correct (84 and 60), with relative frequency × 240 shown |
| 1 | Says (b) is not supported and explains that 0.35 is less than 0.50, so it is not a majority, in context |
| 1 | Says (c) is not supported, with the proportion 0.20 (or 48 residents) compared with 1 in 5 |
Accept 35% and 20% in place of 0.35 and 0.20. In (b), “the pool is the most popular” alone does not earn the point, because it does not answer the claim.
Question 6 (constructed response · stretch)
A fictional music festival sells three types of ticket. The table shows the tickets sold in two years.
| Ticket type | 2025 | 2026 |
|---|---|---|
| Day | 360 | 480 |
| Weekend | 280 | 360 |
| Family | 160 | 360 |
| Total | 800 | 1,200 |
(a) Calculate the relative frequency of each ticket type in each year. (b) The organiser says: “Family tickets have become much more popular: sales more than doubled.” Evaluate this claim. (c) Which graph would let readers compare the two years most fairly? Explain your choice.
Worked solution and suggested Marlbridge rubric
(a) 2025 (n = 800): Day 0.45, Weekend 0.35, Family 0.20. 2026 (n = 1,200): Day 0.40, Weekend 0.30, Family 0.30. Each year’s proportions add to 1.00.
(b) The count did more than double: 360 ÷ 160 = 2.25. But total sales also rose, by a factor of 1,200 ÷ 800 = 1.5, so every type would be expected to sell more. The fair measure of popularity is the proportion of tickets: Family rose from 0.20 to 0.30 of all tickets sold, 1.5 times as large. So Family tickets did become more popular, but “more than doubled” describes the number sold, not the share. Day and Weekend tickets also sold more (by 120 and 80) yet their shares fell by 0.05 each, which shows why counts alone mislead.
(c) A side-by-side relative frequency bar chart, with the 2025 and 2026 bars next to each other for each ticket type and one scale from 0 to 0.50. Relative frequencies remove the effect of the different totals, and bars against one scale make small differences (such as 0.45 against 0.40) easy to see. Two pie charts, one per year, would also be acceptable, since each circle shows that year’s whole; comparing angles is less accurate than comparing heights. A bar chart of the counts would mislead, because the 2026 bars would be taller mainly because more tickets were sold.
| Point | What earns it |
|---|---|
| 1 | All six relative frequencies correct |
| 1 | Notes that the count more than doubled (2.25 times) but total sales also rose (1.5 times) |
| 1 | Uses the proportions (0.20 to 0.30) to conclude that Family tickets did become more popular, though not “more than doubled”, in context |
| 1 | Chooses a graph of relative frequencies (side-by-side bars or two pie charts) and explains why counts would mislead |
Accept percentages in place of proportions. A conclusion with no values quoted does not earn point 3.
Question 7 (explanation · stretch)
A fictional youth club asked 50 members: “Which sports do you play? Tick all that apply.” The numbers of ticks were Football 22, Basketball 18, Swimming 15, Tennis 9 and None 6.
(a) A member wants to show the results in a pie chart. Explain why a pie chart is not appropriate. (b) Describe a suitable graph, giving the value each part of it would show. (c) Another member arranges the bars of a bar chart from tallest to shortest and says: “The distribution of sports is skewed to the right.” Explain what is wrong with this statement.
Model answer and suggested Marlbridge rubric
(a) The ticks add to 22 + 18 + 15 + 9 + 6 = 70, but there are only 50 members. Some members ticked more than one sport, so the categories overlap and do not split the 50 members into separate parts of one whole. The percentages would add to 140%, which a whole circle (100%) cannot show.
(b) A bar chart with one bar per answer, each showing the proportion of the 50 members who gave that answer: Football 22 ÷ 50 = 44%, Basketball 36%, Swimming 30%, Tennis 18%, None 12%. The bars are separate and the vertical axis starts at 0. The bars do not need to add to 100%, and the caption should say that members could choose more than one sport.
(c) Shape words such as “skewed” describe a quantitative variable, whose values have a fixed order on a number line. Sports are categories with no natural order. The member chose to put the bars in order of height; a different order would give a different “shape”. Instead, describe which answers were most and least common: football was the most common answer (44% of members) and tennis was the least common sport (18%).
| Point | What earns it |
|---|---|
| 1 | Explains that members could give more than one answer, so the parts (70 ticks, 140%) add to more than the whole (50 members, 100%) |
| 1 | Describes a bar chart with each bar’s proportion out of the 50 members, with at least two correct values |
| 1 | Explains that categories have no natural order, so skewness has no meaning here, and gives a correct alternative description in context |
How did you do?
- Q1 or Q4 wrong: re-read “Pie charts” in the study guide and Worked example 1. Angle = proportion × 360°; count = proportion × n.
- Q2 wrong: revisit “Graphs that mislead” in “Bar chart or pie chart?”.
- Q3 or Q6 wrong: revisit “Comparing two or more groups” and Worked example 2. Compare proportions when the group sizes differ.
- Q5 wrong: revisit “Using a graph to justify a claim”. “Most common” is not the same as “most”.
- Q7 wrong: revisit the table in “Bar chart or pie chart?” and the last point of “Common misconceptions”.
Then tick off the topic checklist.