S2: Charts & Diagrams
Interpret and construct: tables, bar charts, pie charts, pictograms, vertical line charts, time series
📋 Key Concepts
Definition: Charts and diagrams are visual representations of data that make it easier to understand patterns, trends, and comparisons.
Types of Charts & Diagrams
| Chart Type | Best Used For |
|---|---|
| Bar Chart | Comparing discrete categories |
| Pie Chart | Showing proportions of a whole |
| Pictogram | Simple data for younger audiences |
| Vertical Line Chart | Discrete data with frequency |
| Time Series | Data changes over time |
| Frequency Table | Organising data by categories |
📝 Bar Charts
Features:
- Bars have equal width
- Height represents frequency or value
- Gaps between bars (discrete data)
- Both axes should be labelled
Example 1
The table shows favourite colours of 30 students. Draw a bar chart.
| Colour | Frequency |
|---|---|
| Red | 8 |
| Blue | 12 |
| Green | 5 |
| Yellow | 5 |
Solution:
Draw vertical bars with heights 8, 12, 5, 5. Label axes: "Colour" (x-axis), "Frequency" (y-axis). Include a title: "Favourite Colours of 30 Students".
📝 Pie Charts
Key Facts:
- A full circle = 360°
- Each sector represents a category
- Angle for each category = (frequency ÷ total) × 360°
Example 2
Draw a pie chart for this data showing how 24 students travel to school.
| Method | Frequency |
|---|---|
| Walk | 9 |
| Bus | 8 |
| Car | 5 |
| Cycle | 2 |
Solution:
Total = 24 students
Walk: (9/24) × 360° = 135°
Bus: (8/24) × 360° = 120°
Car: (5/24) × 360° = 75°
Cycle: (2/24) × 360° = 30°
Check: 135 + 120 + 75 + 30 = 360° ✓
Example 3
A pie chart shows that 120° represents dogs. If the total is 360 people, how many chose dogs?
Solution:
Number = (120/360) × 360 = 120 people
Or: 120° is one third of 360°, so dogs = 1/3 of 360 = 120
📝 Pictograms
Features:
- Use symbols or pictures to represent data
- Include a key showing what each symbol represents
- Can use half-symbols for half values
Example 4
Draw a pictogram for books borrowed from a library: Monday 8, Tuesday 12, Wednesday 6. Use 📚 = 4 books.
Solution:
Monday: 📚📚 (8 books = 2 symbols)
Tuesday: 📚📚📚 (12 books = 3 symbols)
Wednesday: 📚📚 (6 books = 1 full + 1 half symbol)
📝 Vertical Line Charts
Features:
- Vertical lines from x-axis to the data value
- Used for discrete data
- Lines have equal spacing
- Height represents frequency
Example 5
Draw a vertical line chart for the number of pets owned by students in a class.
| Pets | 0 | 1 | 2 | 3 |
|---|---|---|---|---|
| Frequency | 6 | 10 | 8 | 4 |
Solution:
Draw vertical lines at each number (0, 1, 2, 3) with heights 6, 10, 8, 4. Add dots at the top of each line.
📝 Time Series
Features:
- Shows how data changes over time
- Points connected by line segments
- Time on x-axis (e.g. months, years)
- Useful for spotting trends
Trend Lines: A line drawn through the data to show the general direction (increasing, decreasing, or stable).
Example 6
The table shows monthly sales (£ thousands). Describe the trend.
| Month | Jan | Feb | Mar | Apr | May | Jun |
|---|---|---|---|---|---|---|
| Sales | 12 | 14 | 13 | 16 | 18 | 20 |
Solution:
Plot points and connect with lines. The trend is upward (increasing) as sales rise from 12 to 20 over the 6 months.
Seasonal Variation: Regular patterns that repeat over time (e.g. ice cream sales higher in summer).
📝 Frequency Tables
Purpose: Organise data by counting how many times each value occurs.
Example 7
Organise this data into a frequency table: 3, 5, 3, 4, 5, 3, 4, 5, 5, 3
Solution:
| Value | Tally | Frequency |
|---|---|---|
| 3 | |||| | 4 |
| 4 | || | 2 |
| 5 | |||| | 4 |
Total = 10 values ✓
❓ Practice Questions
Q1: Calculate the angle for a pie chart sector representing 15 students out of a total of 60.
Q2: A pictogram uses ⭐ = 6 points. How many stars are needed to represent 27 points?
Q3: In a bar chart, what should be the height of the "Blue" bar if 24 people chose blue out of 120 surveyed?
Q4: A pie chart has a sector of 90°. If the total frequency is 200, how many does this sector represent?
Q5: Describe the trend shown in a time series graph where values go: 8, 7, 6, 5, 4, 3 over six months.
✅ Answers
- (15/60) × 360° = 90°
- 27 ÷ 6 = 4.5 stars (4 full stars and 1 half star)
- Height = 24 (the frequency value)
- (90/360) × 200 = 50
- Downward trend (decreasing) - values are falling from 8 to 3 over the six months.
🎯 Exam Tips
- Always label axes and include a title
- Check pie chart angles add up to 360°
- Include a key for pictograms
- For bar charts, ensure bars have equal width with gaps
- Look for trends and patterns in time series
- Read the scale carefully - don't assume it starts at 0
🧠 Problem-Solving Strategies
Problem-Solving
For charts and diagrams: (1) For pie charts, always calculate angles: (frequency/total) × 360°, and check they sum to 360°, (2) For bar charts, ensure bars have equal width with gaps, and label both axes, (3) For time series, draw a trend line to show the overall direction, (4) When reading charts, check the scale carefully — it may not start at 0, (5) For pictograms, always state the key (what one symbol represents).
Multi-Step Problem
A survey of 200 people shows favourite takeaway: Pizza 80, Chinese 50, Indian 40, Fish & Chips 30. (a) Calculate pie chart angles. (b) What percentage chose Chinese? (c) If this data represents a town of 50,000, estimate how many prefer Pizza.
Solution: (a) Pizza: (80/200)×360° = 144°. Chinese: (50/200)×360° = 90°. Indian: (40/200)×360° = 72°. Fish & Chips: (30/200)×360° = 54°. Check: 144+90+72+54 = 360° ✓ (b) 50/200 = 25%. (c) Estimated = (80/200) × 50000 = 20,000.
⚠️ Common Errors
Watch Out!
1. Wrong: In a pie chart, using the frequency as the angle (e.g. drawing 80° for Pizza because the frequency is 80) Correct: Angle = (frequency/total) × 360° — the angle depends on the proportion, not the raw frequency
2. Wrong: Drawing a bar chart with no gaps between bars (that's a histogram for continuous data) Correct: Bar charts have gaps between bars because the data is discrete/categorical
3. Wrong: Reading a chart value by reading the wrong axis or misreading the scale (e.g. each square = 2, not 1) Correct: Always check the scale divisions before reading values — count the squares and work out what each one represents
✍️ 6-Mark Exam Question
Extended Answer
6 marks: The table shows monthly sales for a shop over two years:
| Month | Jan | Feb | Mar | Apr | May | Jun |
|---|---|---|---|---|---|---|
| 2024 | 12 | 14 | 18 | 22 | 26 | 30 |
| 2025 | 15 | 17 | 21 | 25 | 29 | 33 |
(a) Draw a time series graph showing both years. (b) Describe the trend and compare 2024 with 2025. (c) Estimate sales for August 2025, giving a reason for your estimate.
(a) Plot both years on the same axes with months on x-axis and sales (£000s) on y-axis. Connect points within each year. Use different colours or a key for 2024 and 2025.
(b) Both years show an upward trend (increasing sales from January to June). 2025 sales are consistently higher than 2024 by approximately £3000 each month. The rate of increase is similar in both years.
(c) The monthly increase is roughly £4000/month. By August (2 months after June): 33 + 4 + 4 = £41,000. Alternatively, the pattern from 2024 shows growth slows in later months, so a lower estimate of £38,000 may be more realistic.
Mark scheme: M1 for plotting points, A1 for connected time series with key, M1 for describing upward trend, A1 for comparing years, M1 for extrapolation with reason, A1 for reasonable estimate with justification
📊 AO3: Reason & Interpret
Reasoning and Interpretation
A pie chart shows how a school budget of £500,000 is spent: Salaries 210°, Resources 72°, Maintenance 54°, Other 24°.
(a) Calculate the amount spent on Salaries.
(b) What fraction of the budget is spent on Resources?
(c) The headteacher says "We spend more on Salaries than everything else combined." Is this correct? Show working.
Answers: (a) Salaries: (210/360) × £500,000 = £291,667 (b) Resources: 72/360 = 1/5 of the budget (c) Salaries = 210°. Everything else = 72+54+24 = 150°. Since 210° > 150°, the headteacher is correct — Salaries take up more than half the budget.
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🎬 Video Resources
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