Common statistical diagrams
Data can be displayed in several ways, each suited to a different purpose.
- Bar chart — bars of equal width whose heights show frequency; the tallest bar is the mode.
- Pictogram — a picture represents a fixed number of items; part-symbols show part-values.
- Pie chart — a circle split into sectors that show how a whole is shared out.
- Stem-and-leaf diagram — keeps every original value while showing the shape of the data.
Key idea
In a pie chart the angles add up to 360°. For a category: sector angle = (frequency ÷ total) × 360°. Reversing this gives frequency = (angle ÷ 360°) × total.
Worked example
Worked example
30 people are surveyed and 12 choose tea. Find the pie-chart angle for tea.
Angle = (12 ÷ 30) × 360° = 0.4 × 360° = 144°.
Check: a sector of 90° would be (90 ÷ 360) × 30 = 7.5 people, so 144° for 12 people is reasonable.
Stem-and-leaf
A row such as 4 | 2 6 has a stem of 4 (tens) and leaves 2 and 6 (units), representing the values 42 and 46. Because the leaves are ordered, the median can be read directly.
Remember
- A pie chart is best when you want to compare parts of a whole.
- Always include a key on a pictogram and a stem-and-leaf diagram.
- Percentage of a pie = (angle ÷ 360°) × 100.