Corrigé

8.11 Presenting Data

Pack A — Réponses

#	Question	Réponse
1	Which type of chart is best for showing how a whole is divided into parts (e.g. how the school budget is split)?	Pie chart
2	Which chart is most appropriate for comparing the heights of 5 different buildings?	Bar chart
3	Which chart is most appropriate for showing how a temperature changes over a day?	Line chart
4	Which chart is best for continuous numerical data (e.g. heights of 100 pupils grouped into intervals)?	Histogram
5	In a pie chart of 200 students, 80 chose Football. What angle does Football occupy?	144°
6	In a survey of 200 students, 84 preferred Pasta. What angle on a pie chart represents Pasta?	151.2°
7	In a survey of 200 students, 84 preferred Pasta. What percentage preferred Pasta?	42%
8	On a bar chart of favourite fruits, the Apple bar is 12 units tall, representing 24 students. What does 1 unit represent?	2 students
9	A line chart shows temperature: 9 am = 12°C, 12 pm = 18°C, 3 pm = 22°C, 6 pm = 15°C. What was the peak temperature?	22°C at 3 pm
10	Find the midpoint of the class interval 8–11 cm.	9.5 cm
11	A frequency table of grouped data: 0–5 → 4; 5–10 → 7; 10–15 → 6; 15–20 → 3. Find the total students.	20
12	In a pie chart of 30 students, the angles for "Liked Maths" (yes/no) are 168° (yes) and 192° (no). How many said yes?	14
13	A class interval has lower bound 12 and upper bound 15, frequency 7. Find the (a) class width and (b) frequency density.	(a) 3 (b) ≈ 2.33
14	A bar chart of favourite colour shows: Red 12, Blue 18, Green 8. Convert to percentages of the total.	Red 31.6%, Blue 47.4%, Green 21.1% (total 38)
15	On a histogram with class widths 4, the frequencies are 12, 20, 24, 4 for classes 0-4, 4-8, 8-12, 12-16. Find the frequency densities.	3, 5, 6, 1
16	A line graph shows monthly rainfall (mm): Jan 50, Feb 40, Mar 60, Apr 90. Find the (a) total, (b) mean rainfall, (c) month with most rain.	(a) 240 (b) 60 (c) Apr
17	In a pie chart of student transport (n = 240), angles are: Walk 90°, Bus 120°, Car 90°, Cycle 60°. How many students walk?	60
18	For a histogram, if a class has frequency 30 and density 5, what is its class width?	6
19	A bar chart shows daily ice-cream sales: Mon 25, Tue 30, Wed 22, Thu 35, Fri 50. (a) Find the week's total. (b) Find the modal day.	(a) 162 (b) Friday (50)
20	A histogram shows ages 0-20: density 2; 20-40: density 4; 40-60: density 3; 60-80: density 1. Find total frequency (assuming widths of 20).	200
21	A frequency table has classes (8-11), (12-15), (16-19), (20-23), (24-27), (28-31) with frequencies 3, 7, 5, 4, 0, 1. (a) State the modal class. (b) How many students total?	(a) 12-15 (b) 20
22	A bar chart compares 2 datasets: Class A (red bars) and Class B (blue bars), categories Maths, English, Science. The mean scores are A: 75, 68, 80; B: 70, 72, 78. Describe one feature visible from the chart.	A is stronger in Maths but weaker in English; both similar in Science
23	A pie chart of 360 students shows transport: Walk 25%, Bus 35%, Car 30%, Cycle 10%. Find (a) the angle for each slice, (b) the number of students in each category.	(a) 90°, 126°, 108°, 36° (b) 90, 126, 108, 36
24	Construct a pie chart for 30 students whose favourite subjects are: Maths 12, English 9, Science 6, Other 3. State each slice angle.	Maths 144°, English 108°, Science 72°, Other 36°
25	On a histogram with unequal class widths, frequencies 12, 20, 24, 4 correspond to widths 4, 4, 8, 4. Find the densities and identify which class has the tallest bar.	Densities 3, 5, 3, 1. Tallest bar = class 2 (density 5)
26	A line chart shows weekly profits (chf) at a café: Jan 1200, Feb 1500, Mar 1300, Apr 1700, May 1900. Find the (a) mean, (b) range, (c) month with biggest change from prior month.	(a) 1520 (b) 700 (c) April (+400)
27	A stacked bar chart shows boys vs girls in Y7, Y8, Y9: Y7 (boys 100, girls 100), Y8 (90, 90), Y9 (110, 110). Total in each year?	200, 180, 220
28	For the same data (Y7: 200, Y8: 180, Y9: 220), choose between (a) grouped bar, (b) stacked bar, (c) line chart. Which is best for comparing within-year boys vs girls?	Grouped bar — places boys and girls side by side for each year
29	A pie chart slice represents 25% of 800 people. Find (a) the number of people, (b) the angle of the slice.	(a) 200 (b) 90°
30	Choose the most misleading chart for the data: 50 yes, 50 no (a) double bar; (b) pie chart with very different colours; (c) bar chart with y-axis starting at 40.	(c) — truncated axis makes 50 vs 50 look very different
31	A histogram has class widths and frequencies: width 4 → freq 12; width 4 → freq 20; width 8 → freq 24; width 4 → freq 4. (a) Densities for each. (b) Tallest bar.	(a) 3, 5, 3, 1 (b) Density-5 class
32	Construct an infographic comparison: round-trip Geneva-Nice CO₂ per person — Plane 80 kg, Train 15.3 kg, Car (solo) 165.4 kg. Express each as a percentage of the largest, and identify the best chart.	Plane 48.4%, Train 9.3%, Car 100%; bar chart is best
33	A pie chart represents a budget of £24 000 with slices: Salaries 50%, Rent 25%, Supplies 15%, Other 10%. Find the £ amount and angle for each slice.	Salaries 12000/180°, Rent 6000/90°, Supplies 3600/54°, Other 2400/36°
34	A double bar chart compares mean test scores in 2024 and 2025 across 3 schools. School A: 60, 65; B: 70, 72; C: 80, 78. Compute the year-on-year change for each and identify the trend.	A: +5, B: +2, C: -2. Trend: A improved most; C declined.
35	A line chart of crime rates per 1000 over 5 years: 35, 30, 28, 26, 22. Find (a) the percentage decrease from year 1 to 5. (b) Annual rate of decrease (assuming linear).	(a) ≈ 37.1% (b) ≈ 3.25/year
36	A pie chart has slices with angles 90°, 90°, 90°, 90°. (a) Is this misleading or fine? Explain. (b) What does the chart say about the data?	(a) Fine — equal slices for 4 equal-frequency categories. (b) Each category 25% of the whole.
37	A misleading bar chart shows sales: 2024 → 100; 2025 → 110, but the y-axis goes 95 to 115. Discuss why this is misleading and how to fix it.	Y-axis doesn't start at 0 — visual difference exaggerated. Fix: start at 0.
38	For 50 student scores, the relative frequencies are 0–20%: 0.04; 20–40%: 0.12; 40–60%: 0.32; 60–80%: 0.36; 80–100%: 0.16. Construct the frequency table.	Frequencies: 2, 6, 16, 18, 8 (total 50)
39	A line chart of monthly profits shows oscillations between 1000 and 1500 chf throughout the year, but the overall trend is flat. What charts/measures would best convey this?	Show monthly line + a horizontal mean line. Add range and standard deviation.
40	A pie chart and a bar chart present the same data of 4 categories (each 25%). Which is easier to read? Which is more accurate?	Bar chart easier; pie chart accurate but slices hard to compare exactly

Pack B — Réponses

#	Question	Réponse
1	Which type of chart is best for showing how a whole is divided into parts (e.g. how the school budget is split)?	Pie chart (or stacked bar)
2	Which chart is most appropriate for comparing the heights of 5 different buildings?	Bar chart
3	Which chart is most appropriate for showing how a temperature changes over a day?	Line chart
4	Which chart is best for continuous numerical data (e.g. heights of 100 pupils grouped into intervals)?	Histogram
5	In a pie chart of 200 students, 80 chose Football. What angle does Football occupy?	108°
6	In a survey of 200 students, 56 preferred Pasta. What angle on a pie chart represents Pasta?	100.8°
7	In a survey of 200 students, 56 preferred Pasta. What percentage preferred Pasta?	28%
8	On a bar chart of favourite fruits, the Apple bar is 12 units tall, representing 24 students. What does 1 unit represent?	4 students
9	A line chart shows temperature: 9 am = 12°C, 12 pm = 18°C, 3 pm = 22°C, 6 pm = 15°C. What was the peak temperature?	19°C at 3 pm
10	Find the midpoint of the class interval 16–19 cm.	17.5 cm
11	A frequency table of grouped data: 0–5 → 4; 5–10 → 7; 10–15 → 6; 15–20 → 3. Find the total students.	30
12	In a pie chart of 30 students, the angles for "Liked Maths" (yes/no) are 168° (yes) and 192° (no). How many said yes?	16
13	A class interval has lower bound 12 and upper bound 15, frequency 7. Find the (a) class width and (b) frequency density.	(a) 3 (b) ≈ 0.67
14	A bar chart of favourite colour shows: Red 12, Blue 18, Green 8. Convert to percentages of the total.	Red 37.5%, Blue 50%, Green 12.5% (total 40)
15	On a histogram with class widths 4, the frequencies are 12, 20, 24, 4 for classes 0-4, 4-8, 8-12, 12-16. Find the frequency densities.	2, 3, 4, 1
16	A line graph shows monthly rainfall (mm): Jan 50, Feb 40, Mar 60, Apr 90. Find the (a) total, (b) mean rainfall, (c) month with most rain.	(a) 260 (b) 65 (c) Apr
17	In a pie chart of student transport (n = 240), angles are: Walk 90°, Bus 120°, Car 90°, Cycle 60°. How many students walk?	Same.
18	For a histogram, if a class has frequency 30 and density 5, what is its class width?	4
19	A bar chart shows daily ice-cream sales: Mon 25, Tue 30, Wed 22, Thu 35, Fri 50. (a) Find the week's total. (b) Find the modal day.	(a) 143 (b) Friday (45)
20	A histogram shows ages 0-20: density 2; 20-40: density 4; 40-60: density 3; 60-80: density 1. Find total frequency (assuming widths of 20).	220
21	A frequency table has classes (8-11), (12-15), (16-19), (20-23), (24-27), (28-31) with frequencies 3, 7, 5, 4, 0, 1. (a) State the modal class. (b) How many students total?	Same.
22	A bar chart compares 2 datasets: Class A (red bars) and Class B (blue bars), categories Maths, English, Science. The mean scores are A: 75, 68, 80; B: 70, 72, 78. Describe one feature visible from the chart.	Same observation.
23	A pie chart of 360 students shows transport: Walk 25%, Bus 35%, Car 30%, Cycle 10%. Find (a) the angle for each slice, (b) the number of students in each category.	(a) 72°, 144°, 108°, 36° (b) 48, 96, 72, 24
24	Construct a pie chart for 30 students whose favourite subjects are: Maths 12, English 9, Science 6, Other 3. State each slice angle.	Maths 150°, English 105°, Science 75°, Other 30°
25	On a histogram with unequal class widths, frequencies 12, 20, 24, 4 correspond to widths 4, 4, 8, 4. Find the densities and identify which class has the tallest bar.	Same.
26	A line chart shows weekly profits (chf) at a café: Jan 1200, Feb 1500, Mar 1300, Apr 1700, May 1900. Find the (a) mean, (b) range, (c) month with biggest change from prior month.	Same.
27	A stacked bar chart shows boys vs girls in Y7, Y8, Y9: Y7 (boys 100, girls 100), Y8 (90, 90), Y9 (110, 110). Total in each year?	Same.
28	For the same data (Y7: 200, Y8: 180, Y9: 220), choose between (a) grouped bar, (b) stacked bar, (c) line chart. Which is best for comparing within-year boys vs girls?	Same.
29	A pie chart slice represents 25% of 800 people. Find (a) the number of people, (b) the angle of the slice.	(a) 210 (b) 126°
30	Choose the most misleading chart for the data: 50 yes, 50 no (a) double bar; (b) pie chart with very different colours; (c) bar chart with y-axis starting at 40.	Same.
31	A histogram has class widths and frequencies: width 4 → freq 12; width 4 → freq 20; width 8 → freq 24; width 4 → freq 4. (a) Densities for each. (b) Tallest bar.	Same.
32	Construct an infographic comparison: round-trip Geneva-Nice CO₂ per person — Plane 80 kg, Train 15.3 kg, Car (solo) 165.4 kg. Express each as a percentage of the largest, and identify the best chart.	Same.
33	A pie chart represents a budget of £24 000 with slices: Salaries 50%, Rent 25%, Supplies 15%, Other 10%. Find the £ amount and angle for each slice.	Salaries 7200/144°, Rent 5400/108°, Supplies 3600/72°, Other 1800/36°
34	A double bar chart compares mean test scores in 2024 and 2025 across 3 schools. School A: 60, 65; B: 70, 72; C: 80, 78. Compute the year-on-year change for each and identify the trend.	Same.
35	A line chart of crime rates per 1000 over 5 years: 35, 30, 28, 26, 22. Find (a) the percentage decrease from year 1 to 5. (b) Annual rate of decrease (assuming linear).	Same.
36	A pie chart has slices with angles 90°, 90°, 90°, 90°. (a) Is this misleading or fine? Explain. (b) What does the chart say about the data?	Same.
37	A misleading bar chart shows sales: 2024 → 100; 2025 → 110, but the y-axis goes 95 to 115. Discuss why this is misleading and how to fix it.	Same.
38	For 50 student scores, the relative frequencies are 0–20%: 0.04; 20–40%: 0.12; 40–60%: 0.32; 60–80%: 0.36; 80–100%: 0.16. Construct the frequency table.	Same.
39	A line chart of monthly profits shows oscillations between 1000 and 1500 chf throughout the year, but the overall trend is flat. What charts/measures would best convey this?	Same.
40	A pie chart and a bar chart present the same data of 4 categories (each 25%). Which is easier to read? Which is more accurate?	Same.

Problèmes — Solutions détaillées

**Designing a pie chart.** A survey of 360 students on favourite music: | Pop | Rock | Hip-Hop | Classical | Other | |-----|------|---------|-----------|-------| | 144 | 108 | 72 | 18 | 18 | (a) Find the angle for each slice. (b) Find the percentage for each. (c) State the modal category.

Réponse

(a) 144°, 108°, 72°, 18°, 18° (b) 40%, 30%, 20%, 5%, 5% (c) Pop

(a) Multiply each count by $360°/360 = 1$. Angles: 144°, 108°, 72°, 18°, 18°. (b) Each $\text{count}/360 \times 100$: 40%, 30%, 20%, 5%, 5%. (c) Modal = Pop (largest count).

**Histogram with unequal widths.** Data is grouped into: - 0–4: 12 students - 4–8: 20 - 8–16: 24 - 16–20: 4 (a) Find the frequency density for each class. (b) Which class has the tallest bar? (c) Class 8–16 has more students but a shorter bar — explain.

Réponse

(a) 3, 5, 3, 1 (b) Class 4–8 (c) Wider class, same density

(a) Density = freq / width: $12/4 = 3$, $20/4 = 5$, $24/8 = 3$, $4/4 = 1$. (b) Tallest = density 5 = class 4–8. (c) Class 8–16 has width 8 (twice as wide) and 24 students. Density $= 24/8 = 3$. 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.

**Bar vs pie chart comparison.** Data on 200 students' favourite subjects: | Maths | English | Science | History | Art | |-------|---------|---------|---------|-----| | 60 | 50 | 40 | 30 | 20 | (a) Construct a bar chart description (bar heights). (b) Construct a pie chart description (slice angles). (c) Which is easier to read for comparing subjects? (d) Which is easier to read for showing total proportions?

Réponse

(a) 60, 50, 40, 30, 20 (b) 108°, 90°, 72°, 54°, 36° (c) Bar (d) Pie

(a) Bar heights = frequencies: 60, 50, 40, 30, 20. (b) Angles: $\text{count}/200 \times 360°$: 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.

**Line chart: rainfall over a year.** Monthly rainfall (mm) in a town: 45, 38, 52, 60, 72, 80, 85, 90, 75, 65, 55, 48. (a) Sketch a description of the line chart. (b) Identify the wettest month. (c) Find the mean monthly rainfall. (d) Find the annual total.

Réponse

(a) Line peaks in Aug/Sept (b) August (90 mm) (c) ≈ 63.75 mm (d) 765 mm

(a) Line goes up from Jan to Aug, peaks at Aug, declines. (b) Aug 90. (c) Sum 765, mean $765/12 = 63.75$ mm. (d) Annual total 765 mm.

**Choosing the right chart.** For each scenario, choose: (a) bar chart, (b) pie chart, (c) line chart, (d) histogram, (e) scatter plot. (i) Daily temperature over a week. (ii) Favourite ice-cream flavour of 50 students. (iii) Heights of 100 students grouped into intervals. (iv) Comparing sales in 3 different shops. (v) Relationship between hours studied and exam mark.

Réponse

(i) c (ii) a or b (iii) d (iv) a (v) e

(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**.

**Misleading axes.** A newspaper shows a bar chart of crime rates per 1000: 2024 = 28; 2025 = 27. The y-axis starts at 26. (a) What does the chart visually suggest? (b) Compute the actual percentage change. (c) Draw the chart with a y-axis starting at 0 and describe the visual difference. (d) When is a non-zero baseline justified?

Réponse

(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

(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: $(28 - 27)/28 \times 100 \approx 3.6\%$ — 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.

**Grouped bar chart.** A school records year-end average marks for two consecutive years across 3 subjects: | Subject | 2024 | 2025 | |---------|------|------| | Maths | 65 | 70 | | English | 72 | 70 | | Science | 60 | 68 | (a) Construct a grouped bar chart description. (b) Find the percentage change for each subject. (c) Find the school's overall average for each year.

Réponse

(a) Three pairs of bars, side by side, one for each year. (b) Maths: $(70-65)/65 \times 100 \approx 7.7\%$. English: $(70-72)/72 \times 100 \approx -2.8\%$. Science: $(68-60)/60 \approx 13.3\%$. (c) 2024 mean = $(65 + 72 + 60)/3 = 65.67$. 2025 mean = $(70 + 70 + 68)/3 = 69.33$. Overall improvement of 3.66.

**Frequency table to histogram.** Reaction distances (cm) for 20 students: | Class | 8–11 | 12–15 | 16–19 | 20–23 | 24–27 | 28–31 | |-------|------|-------|-------|-------|-------|-------| | Frequency | 3 | 7 | 5 | 4 | 0 | 1 | (a) State the class width (assume equal widths). (b) State the modal class. (c) Describe the histogram shape. (d) Identify any outlier classes.

Réponse

(a) 4 (b) 12-15 (c) Right-skewed (long tail) (d) Class 28-31 (frequency 1, isolated)

(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.

**Pie chart calculation.** A pie chart shows the budget of a school: Teachers 60%, Buildings 20%, Supplies 10%, Other 10%. Total annual budget is £600 000. (a) Find the £ allocated to each category. (b) Find the angle of each slice. (c) Compute the percentage of the budget not used for teachers.

Réponse

(a) 360k, 120k, 60k, 60k (b) 216°, 72°, 36°, 36° (c) 40%

(a) Apply percentages: 360 000, 120 000, 60 000, 60 000. (b) Angles: 216°, 72°, 36°, 36° (sum 360°). (c) 100% - 60% = 40%.

**Constructing a histogram.** Heights of 50 plants (cm) are grouped: | Class | Freq | |-------|------| | 5–10 | 4 | | 10–15 | 8 | | 15–20 | 18 | | 20–25 | 12 | | 25–30 | 8 | (a) State the class width. (b) Compute the frequency densities. (c) State the modal class. (d) Estimate the mean height using midpoints.

Réponse

(a) 5 (b) 0.8, 1.6, 3.6, 2.4, 1.6 (c) 15-20 (d) 18.5

(a) Width 5. (b) Densities: $4/5, 8/5, 18/5, 12/5, 8/5$ = 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. $\sum fm = 30 + 100 + 315 + 270 + 220 = 935$. Mean $= 935/50 = 18.7$.

**Comparing line charts.** Two stocks' monthly prices (chf): | Month | A | B | |-------|---|---| | Jan | 100 | 100 | | Feb | 110 | 95 | | Mar | 105 | 90 | | Apr | 115 | 85 | | May | 120 | 80 | (a) Identify the overall trend for each. (b) Find the percentage change for each. (c) Which would you invest in?

Réponse

(a) A rising, B falling (b) A +20%, B -20% (c) A

(a) A rises overall; B declines. (b) A: $(120-100)/100 = +20\%$. B: $(80-100)/100 = -20\%$. (c) A — positive trend.

**Visual literacy.** Identify the issue in each chart description. (a) A pie chart with 15 slices, including 8 slices each of "Other". (b) A bar chart with no y-axis label. (c) A line chart connecting non-time-series data (favourite colour vs frequency). (d) A histogram with overlapping class intervals.

Réponse

(a) Too many slices — combine "Other" (b) Missing label (c) Wrong chart type — should be bar (d) Overlapping bins

(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.