8.11 Presenting Data

**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.

**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.

**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?

**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.

**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.

**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?

**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.

**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.

**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.

**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.

**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?

**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.