← Review packs
Solutions — Full Answer Key
MathematicsYear 8 · 8.11 Presenting Data
Solutions · Full Answer Key
Pack A answers · Pack B answers · Problem-solving worked solutions
Pack A — Answers
Bronze
1.Pie chart
2.Bar chart
3.Line chart
4.Histogram
5.144°
6.151.2°
7.42%
8.2 students
9.22°C at 3 pm
10.9.5 cm
Silver
11.20
12.14
13.(a) 3 (b) ≈ 2.33
14.Red 31.6%, Blue 47.4%, Green 21.1% (total 38)
15.3, 5, 6, 1
16.(a) 240 (b) 60 (c) Apr
17.60
18.6
19.(a) 162 (b) Friday (50)
20.200
Gold
21.(a) 12-15 (b) 20
22.A is stronger in Maths but weaker in English; both similar in Science
23.(a) 90°, 126°, 108°, 36° (b) 90, 126, 108, 36
24.Maths 144°, English 108°, Science 72°, Other 36°
25.Densities 3, 5, 3, 1. Tallest bar = class 2 (density 5)
26.(a) 1520 (b) 700 (c) April (+400)
27.200, 180, 220
28.Grouped bar — places boys and girls side by side for each year
29.(a) 200 (b) 90°
30.(c) — truncated axis makes 50 vs 50 look very different
Platinum
31.(a) 3, 5, 3, 1 (b) Density-5 class
32.Plane 48.4%, Train 9.3%, Car 100%; bar chart is best
33.Salaries 12000/180°, Rent 6000/90°, Supplies 3600/54°, Other 2400/36°
34.A: +5, B: +2, C: -2. Trend: A improved most; C declined.
35.(a) ≈ 37.1% (b) ≈ 3.25/year
36.(a) Fine — equal slices for 4 equal-frequency categories. (b) Each category 25% of the whole.
37.Y-axis doesn't start at 0 — visual difference exaggerated. Fix: start at 0.
38.Frequencies: 2, 6, 16, 18, 8 (total 50)
39.Show monthly line + a horizontal mean line. Add range and standard deviation.
40.Bar chart easier; pie chart accurate but slices hard to compare exactly
Pack B — Answers
Bronze
1.Pie chart (or stacked bar)
2.Bar chart
3.Line chart
4.Histogram
5.108°
6.100.8°
7.28%
8.4 students
9.19°C at 3 pm
10.17.5 cm
Silver
11.30
12.16
13.(a) 3 (b) ≈ 0.67
14.Red 37.5%, Blue 50%, Green 12.5% (total 40)
15.2, 3, 4, 1
16.(a) 260 (b) 65 (c) Apr
17.Same.
18.4
19.(a) 143 (b) Friday (45)
20.220
Gold
21.Same.
22.Same observation.
23.(a) 72°, 144°, 108°, 36° (b) 48, 96, 72, 24
24.Maths 150°, English 105°, Science 75°, Other 30°
25.Same.
26.Same.
27.Same.
28.Same.
29.(a) 210 (b) 126°
30.Same.
Platinum
31.Same.
32.Same.
33.Salaries 7200/144°, Rent 5400/108°, Supplies 3600/72°, Other 1800/36°
34.Same.
35.Same.
36.Same.
37.Same.
38.Same.
39.Same.
40.Same.
Problem-solving — Worked Solutions
1Problem 1
Answer
(a) 144°, 108°, 72°, 18°, 18° (b) 40%, 30%, 20%, 5%, 5% (c) Pop
Full working
(a) Multiply each count by . Angles: 144°, 108°, 72°, 18°, 18°.
(b) Each : 40%, 30%, 20%, 5%, 5%.
(c) Modal = Pop (largest count).
(b) Each : 40%, 30%, 20%, 5%, 5%.
(c) Modal = Pop (largest count).
2Problem 2
Answer
(a) 3, 5, 3, 1 (b) Class 4–8 (c) Wider class, same density
Full working
(a) Density = freq / width: , , , .
(b) Tallest = density 5 = class 4–8.
(c) Class 8–16 has width 8 (twice as wide) and 24 students. Density . Class 0–4 with 12 students has the same density. In histograms, **area** represents frequency, so wider bars need to be shorter for the same count.
(b) Tallest = density 5 = class 4–8.
(c) Class 8–16 has width 8 (twice as wide) and 24 students. Density . Class 0–4 with 12 students has the same density. In histograms, **area** represents frequency, so wider bars need to be shorter for the same count.
3Problem 3
Answer
(a) 60, 50, 40, 30, 20 (b) 108°, 90°, 72°, 54°, 36° (c) Bar (d) Pie
Full working
(a) Bar heights = frequencies: 60, 50, 40, 30, 20.
(b) Angles: : 108°, 90°, 72°, 54°, 36°.
(c) Bar chart is easier for comparing magnitudes (bar length is precise to read).
(d) Pie chart emphasises "what fraction of the whole" each category represents.
(b) Angles: : 108°, 90°, 72°, 54°, 36°.
(c) Bar chart is easier for comparing magnitudes (bar length is precise to read).
(d) Pie chart emphasises "what fraction of the whole" each category represents.
4Problem 4
Answer
(a) Line peaks in Aug/Sept (b) August (90 mm) (c) ≈ 63.75 mm (d) 765 mm
Full working
(a) Line goes up from Jan to Aug, peaks at Aug, declines.
(b) Aug 90.
(c) Sum 765, mean mm.
(d) Annual total 765 mm.
(b) Aug 90.
(c) Sum 765, mean mm.
(d) Annual total 765 mm.
5Problem 5
Answer
(i) c (ii) a or b (iii) d (iv) a (v) e
Full working
(i) Time-series → **line chart**.
(ii) Categorical data → **bar chart** (best for comparing) or **pie chart** (best for proportions).
(iii) Continuous grouped data → **histogram**.
(iv) Comparing discrete categories → **bar chart**.
(v) Two numerical variables → **scatter plot**.
(ii) Categorical data → **bar chart** (best for comparing) or **pie chart** (best for proportions).
(iii) Continuous grouped data → **histogram**.
(iv) Comparing discrete categories → **bar chart**.
(v) Two numerical variables → **scatter plot**.
6Problem 6
Answer
(a) Big drop (b) ≈ 3.6% (c) Bars look almost the same (d) For tiny relative changes where the baseline carries no meaning — but always note the baseline
Full working
(a) The two bars look very different — 2 units (28-26=2) vs 1 unit (27-26=1). Visually appears like crime halved.
(b) Actual change: — tiny.
(c) With y-axis at 0, both bars look nearly identical (28 vs 27).
(d) Acceptable if the chart is clearly annotated and the baseline has meaning (e.g. starting at 36.5°C for fever-monitoring). Otherwise always start at 0.
(b) Actual change: — tiny.
(c) With y-axis at 0, both bars look nearly identical (28 vs 27).
(d) Acceptable if the chart is clearly annotated and the baseline has meaning (e.g. starting at 36.5°C for fever-monitoring). Otherwise always start at 0.
7Problem 7
Answer
(a) 6 bars side by side (b) Maths +7.7%, English -2.8%, Science +13.3% (c) 2024: 65.67; 2025: 69.33
Full working
(a) Three pairs of bars, side by side, one for each year.
(b) Maths: . English: . Science: .
(c) 2024 mean = . 2025 mean = . Overall improvement of 3.66.
(b) Maths: . English: . Science: .
(c) 2024 mean = . 2025 mean = . Overall improvement of 3.66.
8Problem 8
Answer
(a) 4 (b) 12-15 (c) Right-skewed (long tail) (d) Class 28-31 (frequency 1, isolated)
Full working
(a) Width = 4 (e.g. 12 to 15 spans 4 values).
(b) Modal class = 12-15.
(c) Histogram bars rise to a peak at 12-15 then taper off — slight right skew, with a gap in 24-27 and a small tail at 28-31.
(d) The single isolated value in 28-31 is a potential outlier.
(b) Modal class = 12-15.
(c) Histogram bars rise to a peak at 12-15 then taper off — slight right skew, with a gap in 24-27 and a small tail at 28-31.
(d) The single isolated value in 28-31 is a potential outlier.
9Problem 9
Answer
(a) 360k, 120k, 60k, 60k (b) 216°, 72°, 36°, 36° (c) 40%
Full working
(a) Apply percentages: 360 000, 120 000, 60 000, 60 000.
(b) Angles: 216°, 72°, 36°, 36° (sum 360°).
(c) 100% - 60% = 40%.
(b) Angles: 216°, 72°, 36°, 36° (sum 360°).
(c) 100% - 60% = 40%.
10Problem 10
Answer
(a) 5 (b) 0.8, 1.6, 3.6, 2.4, 1.6 (c) 15-20 (d) 18.5
Full working
(a) Width 5.
(b) Densities: = 0.8, 1.6, 3.6, 2.4, 1.6.
(c) Modal class = 15-20.
(d) Midpoints 7.5, 12.5, 17.5, 22.5, 27.5. . Mean .
(b) Densities: = 0.8, 1.6, 3.6, 2.4, 1.6.
(c) Modal class = 15-20.
(d) Midpoints 7.5, 12.5, 17.5, 22.5, 27.5. . Mean .
11Problem 11
Answer
(a) A rising, B falling (b) A +20%, B -20% (c) A
Full working
(a) A rises overall; B declines.
(b) A: . B: .
(c) A — positive trend.
(b) A: . B: .
(c) A — positive trend.
12Problem 12
Answer
(a) Too many slices — combine "Other" (b) Missing label (c) Wrong chart type — should be bar (d) Overlapping bins
Full working
(a) **Too many slices** — readers can't compare. Combine small slices into one "Other".
(b) **Missing axis label** — readers can't tell what's measured.
(c) **Wrong chart** — line charts imply continuous transitions; categorical data needs a bar chart.
(d) **Overlapping bins** — a value at the boundary belongs to two classes. Use mutually exclusive intervals.
(b) **Missing axis label** — readers can't tell what's measured.
(c) **Wrong chart** — line charts imply continuous transitions; categorical data needs a bar chart.
(d) **Overlapping bins** — a value at the boundary belongs to two classes. Use mutually exclusive intervals.