Statistical diagrams: tables, bar charts, pie charts, pictograms
OCR J560 Statistics questions across J560/02 and J560/03 require students to read AND draw diagrams. Marks are awarded for accurate construction (correct angles for pie charts, axis scales for bar charts).
Frequency tables
A frequency table organises data into categories or class intervals. For grouped data:
| Time t (min) | Frequency |
|---|---|
| 0 ≤ t < 10 | 8 |
| 10 ≤ t < 20 | 14 |
| 20 ≤ t < 30 | 6 |
The notation 0 ≤ t < 10 means 0 is included, 10 is not.
Bar charts
Used for discrete or categorical data.
- Bars of equal width with gaps between bars (gaps distinguish bar charts from histograms).
- Vertical axis = frequency; horizontal axis = category.
- Label both axes with the variable name.
- Title the chart.
Comparative bar chart: groups two or more datasets side-by-side. Use a key.
Pie charts
Used to show proportions within a whole. Each slice's angle = (frequency/total) × 360°.
Example: 60 students surveyed, 24 chose football. Football angle = (24/60) × 360 = 144°.
To draw a pie chart:
- Compute angles (must sum to 360°).
- Use a protractor to mark each angle.
- Label slices with category and either frequency or percentage.
To read a pie chart, given the total: frequency = (angle/360) × total.
Pictograms
Used for small datasets. A symbol represents n items, a half-symbol represents n/2, etc.
- Always include a key (e.g. "🍎 = 5 apples").
- Symbols must be the same size and equally spaced.
Choosing the right chart
- Bar chart: comparing categories.
- Pie chart: showing proportions of a whole.
- Pictogram: small dataset, eye-catching for young audiences.
- Line graph: data over time (continuous).
- Histogram: continuous grouped data with possibly unequal class widths (Higher only).
- Frequency polygon: comparing distributions of grouped data.
OCR mark scheme conventions
- Pie chart: B1 for correct total angle calculation; B1 each for correctly drawn slices (within ±2°); B1 for correct labelling.
- Bar chart: B1 for axes correctly labelled; B1 for bars at correct heights; B1 for category labels.
- "Calculate the angle for…" — show the fraction × 360 explicitly for M1.
⚠Common mistakes
- Bars touching (looks like a histogram) — bar charts have gaps.
- Pie chart angles not summing to 360° — check totals.
- Forgetting a key on a pictogram.
- Choosing the wrong scale on the bar chart vertical axis (should be linear).
AI-generated · claude-opus-4-7 · v3-ocr-maths-leaves