Organising data & statistical charts · Ages 12–13
Combined charts, pie charts and line graphs
Angle = count ÷ total × 360°; a combined chart's two axes read apart.
How to do it
Method
Angle = count ÷ total × 360°; a combined chart's two axes read apart
15 ÷ 60 × 360° = 90°
Another way
As a percentage first
90 ÷ 360 = 25%
In full
A combined chart draws a bar chart and a line graph in one picture, with a vertical axis on each side: read a bar against the left axis and a point on the line against the right, after checking the key. Say the bars are each month's mean temperature (left axis, °C) and the line its rainfall (right axis, mm). In a pie chart each sector's angle at the centre = its count ÷ the total × 360°: 15 of 60 choosing basketball make 15 ÷ 60 × 360° = 90°. The other way, a 72° sector standing for 18 people means a total of 18 ÷ (72° ÷ 360°) = 90. A line graph shows a trend: rising is increasing, and the steepest piece is the biggest rise, the later point less the earlier. Choosing a chart: bars to compare amounts, a line graph for change over time, a pie chart for parts of a whole, compound bars or a combined chart for two sets together. Another way for a pie chart: turn the angle into a percentage first, 90° being 90 ÷ 360 = 25%.
Worked examples
Have a go first, then open each one for the answer and the working.
Example 1
A pie chart shows how a group of people most often travel. The 'bus' sector has an angle of 44° at the centre and stands for 11 people. How many people does the whole chart stand for?
Show the answer and working
Answer: 90
44° is 44 ÷ 360 of the full 360°, so the total = 11 ÷ (44 ÷ 360) = 90. Or find how many 1° stands for first.
Example 2
Tsz-ching wants to show how their weight changes month by month over a year. Which statistical chart suits it best?
- A. A stem-and-leaf diagram
- B. A compound bar chart
- C. A line graph
- D. A pie chart
Choose the right answer
Show the answer and working
Answer: C. A line graph
To see one quantity change over time, rising and falling, a line graph shows it most clearly.
Example 3
The combined chart shows a place's mean temperature (bars, left axis, °C) and rainfall (line, right axis, mm) for each month from January to May. In the month with the highest mean temperature, what is the rainfall, in mm?
Show the answer and working
Answer: 200 mm
Find the tallest bar first (25°C on the left axis), then that month's point on the line, read on the right axis: 200 mm.
Practice questions to try
Try these 5; the answers are at the end. For a whole worksheet, see VIP worksheets below.
1.The combined chart shows a place's mean temperature (bars, left axis, °C) and rainfall (line, right axis, mm) for each month from January to May. What is the rainfall in month 1, in mm?
Answer:
2.A pie chart shows the favourite sports of 45 club members, 8 of whom like swimming best. What is the angle at the centre of the swimming sector, in degrees?
Answer:
3.Ka-lok wants to show how their weight changes month by month over a year. Which statistical chart suits it best?
- A. A line graph
- B. A pie chart
- C. A compound bar chart
- D. A stem-and-leaf diagram
Choose the right answer
Answer:
4.A pie chart shows how a group of people most often travel. The 'bus' sector has an angle of 288° at the centre and stands for 16 people. How many people does the whole chart stand for?
Answer:
5.The line graph shows a small shop's takings each month from January to June (thousands of dollars). From one month to the next, what is the biggest rise, in thousands of dollars?
Answer:
All the answers
- 1. 150 mm
- 2. 64°
- 3. A. A line graph
- 4. 20
- 5. 60 thousand dollars
VIP practice notes and papers
Aimed at tests and exams: questions on this topic, new every time, to print or save as a PDF.
- Practice notes: The key point, worked examples step by step, then questions of the same kind to follow, hints fading
- Practice paper: Set out in parts like a school paper, marked, with answers and full working
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