Choosing and reading the right chart
Statistics charts each emphasise something different. Pick the right tool for the data type and you'll communicate clearly; pick the wrong one and you'll mislead.
Frequency tables
The starting point. Two columns: outcome (or class) and frequency.
| Sport | Frequency |
|---|---|
| Football | 14 |
| Tennis | 9 |
| Hockey | 7 |
| Other | 10 |
Total = 40. Use this to build any of the charts below.
Bar charts
For categorical data (or discrete numerical data with few values).
- Equal-width bars, gaps between them.
- Vertical axis: frequency (or relative frequency).
- Horizontal axis: categories.
Worked example: bars of heights 14, 9, 7, 10 for the four sports above.
When comparing two groups (e.g. boys/girls), use a dual (clustered) or stacked bar chart.
Pie charts
For showing shares of a whole. Each slice's angle = (frequency / total) × 360°.
Sport pie chart from the data above:
- Football: (14/40) × 360 = 126°.
- Tennis: (9/40) × 360 = 81°.
- Hockey: (7/40) × 360 = 63°.
- Other: (10/40) × 360 = 90°.
Check the angles sum to 360°. (126 + 81 + 63 + 90 = 360 ✓.)
⚠ Pie charts only show proportions. To convey absolute numbers, label slices with frequencies.
Pictograms
Each symbol represents a fixed number (e.g. one ☆ = 5 votes). Use half/quarter symbols for partial values. Always include a key.
Pictograms are visual and accessible but tricky for fractional values; use them for whole-number-friendly data.
Reading charts to estimate
Given a bar chart, you can read off frequencies and compute things like:
- Total frequency (sum of bars).
- Mean for grouped data (we cover this in S4 with class midpoints).
- Mode (tallest bar).
For pie charts, given the total and an angle:
Frequency = (angle / 360) × total.
Choosing the right chart
| Goal | Chart |
|---|---|
| Compare absolute frequencies of categories | Bar chart |
| Show shares of a single whole | Pie chart |
| Communicate to a non-technical audience | Pictogram |
| Show distribution of grouped numerical data | Histogram (S3) |
| Show change over time | Line graph |
| Show relationship between two numerical variables | Scatter graph (S6) |
✦Worked example— Worked example — pie chart from raw data
35 students were asked about lunch. Results: school dinner 14, packed 12, no lunch 4, café 5. Compute the angles.
Total = 35.
- 14/35 × 360 = 144°.
- 12/35 × 360 = 123.4° (round if needed).
- 4/35 × 360 = 41.1°.
- 5/35 × 360 = 51.4°.
Sum check: 360°. (144 + 123.4 + 41.1 + 51.4 = 359.9 — rounding accounts for the 0.1°.)
⚠Common mistakes— Common mistakes (examiner traps)
- Pie chart angles that don't sum to 360°. Always check.
- Bar chart with unequal bar widths — visually misleading.
- Pictogram missing a key — meaningless without the symbol legend.
- Truncated y-axis that exaggerates differences. Examiners spot this and ask you to comment.
- Pie chart without slice labels — viewers can't read absolute counts.
➜Try this— Quick check
A pie chart shows that 42% of a group prefer chocolate ice cream. The whole pie represents 250 people. How many prefer chocolate?
- 0.42 × 250 = 105 people.
AI-generated · claude-opus-4-7 · v3-deep-statistics