IGCSE Maths · Statistics · Core & Extended

Statistical Charts and Scatter Diagrams

Five ways to picture data at a glance — each suited to a different kind of story. This content is identical for Core and Extended.

1. Bar Charts

Reading a bar chart Apple Banana Orange Mango 18 A bar chart’s height represents frequency — bars are equally spaced with gaps between them (unlike a histogram, covered later, where bars touch).
Try it — Bar Charts (using the chart above)
  1. Which fruit was most popular?
  2. Estimate the frequency for Orange.
  3. If the total surveyed was 54 people, and Apple, Banana, Mango account for 45 of them, find the frequency for Orange.
Show answers
  1. Banana
  2. Approximately 9
  3. 54−45 = 9

2. Pie Charts

Each category’s sector angle is proportional to its frequency, out of the full 360°.

Sector angle = (category frequency ÷ total frequency) × 360°
Worked example 144° 108° 72° 36° A survey of 50 people’s favourite sport: Football 20, Basketball 15, Tennis 10, Swimming 5. Find each sector’s angle.
Football: (20/50)×360 = 144°   Basketball: (15/50)×360 = 108°   Tennis: (10/50)×360 = 72°   Swimming: (5/50)×360 = 36°
Check: 144+108+72+36 = 360° ✓
Try it — Pie Charts
  1. A pie chart shows 40 people’s transport choices: Car 18, Bus 12, Walk 10. Find each sector’s angle.
  2. A pie chart sector is 90°, representing 15 people. Find the total number of people surveyed.
Show answers
  1. Car: (18/40)×360=162°. Bus: (12/40)×360=108°. Walk: (10/40)×360=90°
  2. 90° is a quarter of 360°, so 15 people = ¼ of the total → total = 60

3. Pictograms

A pictogram uses repeated symbols to represent frequency, with a key stating what each symbol (and any partial symbol) is worth.

Worked example A pictogram’s key states: 1 symbol = 4 books. Monday’s row shows 3 full symbols and 1 half symbol. Find the number of books sold on Monday.
3 × 4 + 0.5 × 4 = 12 + 2 = 14 books
Try it — Pictograms
  1. A key states 1 symbol = 6 items. A row shows 2 full symbols and a quarter symbol. Find the total.
  2. A row represents 27 items, and the key is 1 symbol = 6 items. How many full symbols and what fraction of a symbol should be drawn?
Show answers
  1. 2×6 + 0.25×6 = 12+1.5 = 13.5
  2. 27÷6 = 4.5, so 4 full symbols and a half symbol

4. Stem-and-Leaf Diagrams

A stem-and-leaf diagram splits each value into a “stem” (leading digit(s)) and a “leaf” (last digit), keeping every original value visible — unlike a bar chart or pie chart, no detail is lost. A key is always required to show what a stem-leaf pair represents.

Worked example
StemLeaf
19
23  5
31  4  4
42  5
Key: 1 | 9 means 19
This represents the ages 19, 23, 25, 31, 34, 34, 42, 45. Find the median, mode, and range.
Median (8 values, average the middle two): sorted list is already shown; middle two are 31, 34 → (31+34)/2 = 32.5
Mode = 34 (appears twice)    Range = 45 − 19 = 26
Try it — Stem-and-Leaf (using the diagram above)
  1. How many values are in this data set?
  2. Find P(a randomly chosen value is greater than 30).
Show answers
  1. 8 values
  2. Values over 30: 31,34,34,42,45 = 5 out of 8 → 5/8

5. Scatter Diagrams and Correlation

A scatter diagram plots pairs of related values to reveal whether a relationship (correlation) exists between them.

TypeMeaning
Positive correlationAs one variable increases, so does the other
Negative correlationAs one variable increases, the other decreases
No correlationNo clear relationship between the variables
Worked example Hours studied Test score This scatter diagram shows hours studied vs. test score for 8 students. Describe the correlation.
As hours studied increases, test scores generally increase too — this is positive correlation.
Try it — Correlation
  1. Describe the likely correlation between “hours spent watching TV” and “time spent on homework.”
  2. Describe the likely correlation between “a car’s engine size” and “the colour of the car.”
Show answers
  1. Negative correlation — likely, more TV time often means less homework time (though this isn’t guaranteed for every individual).
  2. No correlation — engine size and paint colour have no meaningful relationship.

6. Line of Best Fit

A line of best fit is drawn by eye through the middle of a scatter of points, capturing the overall trend — used to estimate values between (interpolation) or beyond (extrapolation) the plotted data.

Worked example — using the line from Section 5 Using the line of best fit, estimate the test score for a student who studies 4.5 hours.
Reading from the graph at x=4.5 hours, the line gives a score of approximately 69.
This is interpolation — 4.5 hours sits within the range of the original data (1 to 8 hours), so this estimate is reasonably reliable.
Try it — Line of Best Fit
  1. Using the same line, estimate the score for a student who studies 2.5 hours.
  2. Explain why estimating the score for 15 hours of study (using the same line) would be far less reliable.
Show answers
  1. Approximately 58 (reading the line at x=2.5)
  2. This is extrapolation — 15 hours is well beyond the original data range (1–8 hours), and there’s no evidence the same trend continues that far; the relationship could level off, change direction, or behave completely differently.
Common mistakes to watch for
  • Leaving gaps between bars in a bar chart missing, or drawing bars touching (that’s a histogram convention, covered separately) — check which is actually being asked for.
  • Forgetting to check that pie chart angles sum to exactly 360°.
  • Forgetting a pictogram’s key, or using an inconsistent value for partial symbols.
  • Forgetting to include a key for a stem-and-leaf diagram — without it, the diagram is ambiguous (does “3 | 4” mean 34, or something else entirely?).
  • Extrapolating far beyond the range of the original data and treating the estimate as equally reliable as an interpolated one.

7. Quick-Fire Challenge Round

True or False?
  1. Pie chart sector angles must always sum to 360°.
  2. A stem-and-leaf diagram doesn’t need a key, since it’s usually obvious.
  3. Positive correlation means as one variable increases, the other also increases.
  4. Extrapolation is just as reliable as interpolation.
Show answers
  1. True.
  2. False — a key is always required, since stem-and-leaf notation isn’t self-explanatory without one.
  3. True.
  4. False — extrapolating beyond the data range is much less reliable than interpolating within it.
Spot the Error
  1. “A pie chart has sectors 120°, 90°, 100°, and 50°.”
  2. “A pictogram key is 1 symbol = 5 items. A row of 2.5 symbols represents 10 items.”
  3. “There’s clearly negative correlation between shoe size and reading ability in adults, since bigger-footed people read less.”
Show answers
  1. 120+90+100+50 = 360… let me recheck: that’s actually 360, so this one isn’t an error! Always check the numbers rather than assuming.
  2. 2.5 symbols × 5 = 12.5, not 10 — the arithmetic doesn’t match.
  3. There’s no genuine causal or correlational relationship between shoe size and reading ability in adults — any apparent pattern in a small sample would just be coincidence (this one’s a classic example of confusing correlation with a nonsensical, unrelated claim).

8. Mixed Practice — Bringing It All Together

  1. A pie chart shows 60 people’s pet ownership: Dog 24, Cat 21, Other 15. Find each sector’s angle.
  2. A pictogram key is 1 symbol = 8 items. A row shows 3 symbols and three-quarters of a symbol. Find the total.
  3. Describe the correlation you’d expect between “age of a car” and “its resale value.”
Show answers
  1. Dog: (24/60)×360=144°. Cat: (21/60)×360=126°. Other: (15/60)×360=90°
  2. 3×8 + 0.75×8 = 24+6 = 30
  3. Negative correlation — as a car gets older, its resale value generally decreases.

Practice at Home

A large set again — take it steadily.

Part A — Bar charts and pie charts
  1. A pie chart shows 45 people’s favourite drink: Tea 18, Coffee 15, Juice 12. Find each sector’s angle.
  2. A pie chart sector is 60°, representing 8 people. Find the total surveyed.
Part B — Pictograms
  1. A key is 1 symbol = 10 items. A row shows 4 symbols and a fifth of a symbol. Find the total.
  2. A row represents 35 items, key 1 symbol = 10. State the number of full symbols and the fraction needed.
Part C — Stem-and-leaf diagrams
  1. Data: 12, 15, 15, 21, 27, 29, 33, 38. Construct a stem-and-leaf diagram (stems 1, 2, 3), and find the median.
  2. Using your diagram, find the mode and the range.
Part D — Scatter diagrams and correlation
  1. Describe the likely correlation between “outdoor temperature” and “hot chocolate sales.”
  2. Describe the likely correlation between “a student’s shoe size” and “their exam score.”
  3. A line of best fit has equation y = 4x + 20 (from a scatter diagram relating x and y). Estimate y when x=6, and explain whether this is interpolation or extrapolation if the original data ranged from x=1 to x=10.
Part E — Applied / challenge
  1. A pie chart shows exam grades for 72 students: A (72°), B (108°), C (?), with the rest being D. If 20 students got a C, find the angle for D.
  2. Explain why a stem-and-leaf diagram is often more useful than a bar chart when you also need to find the exact median of a data set.
  3. A scatter diagram of “hours of sleep” vs “reaction time (ms)” shows a negative correlation. Explain in context what this means, and suggest one reason (other than sleep directly causing it) why this correlation might appear in real data.

Key Vocabulary Recap

Pictogram — a chart using repeated symbols, with a key
Stem-and-leaf diagram — splits values into stems and leaves, keeping all data visible
Correlation — a relationship between two variables (positive, negative, or none)
Line of best fit — a line drawn to capture a scatter diagram’s overall trend
Interpolation / extrapolation — estimating within / beyond the range of known data

Syllabus Reference

This note covers Cambridge IGCSE Mathematics (0580) sections C9.4 and C9.5 (Core subject content) and sections E9.4 and E9.5 (Extended subject content) — Statistical charts and diagrams, and Scatter diagrams. The wording of these sections is identical for both tiers. Cumulative frequency diagrams and histograms (both Extended-only) are covered in a third and final Statistics note.

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