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Problem-solving Pack
MathematicsYear 8 · 8.11 Presenting Data
Problem-solving Pack
Name: _________________________________
Date: _________________ Class: ___________
These problems are designed to challenge you. Read each question carefully. Show all your reasoning — a correct answer without working receives no credit.
1Problem 1 of 12
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.
| 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.
Working space
2Problem 2 of 12
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.
- 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.
Working space
3Problem 3 of 12
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?
| 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?
Working space
4Problem 4 of 12
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.
(a) Sketch a description of the line chart.
(b) Identify the wettest month.
(c) Find the mean monthly rainfall.
(d) Find the annual total.
Working space
5Problem 5 of 12
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.
(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.
Working space
6Problem 6 of 12
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?
(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?
Working space
7Problem 7 of 12
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.
| 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.
Working space
8Problem 8 of 12
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.
| 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.
Working space
9Problem 9 of 12
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.
(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.
Working space
10Problem 10 of 12
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.
| 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.
Working space
11Problem 11 of 12
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?
| 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?
Working space
12Problem 12 of 12
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.
(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.
Working space