3
Reading pie charts and choosing a graph for the data
Mathematics Prep 1 Term 1, Unit 3, Lesson 3
GoalRead numbers and percents from a pie chart and choose the best graph for the data.
New words
sector angle · the central angle of one sectorbar graph · bars that compare exact values of categorieshistogram · touching columns for data grouped in intervalstotal · the whole amount that the circle stands for
Explanation
To read a pie chart, find what the whole is. A sector with the angle a stands for a/360 of the total, so number = angle ÷ 360° × total, and percent = angle ÷ 360° × 100. If a sector shows p%, the number is p% of the total. Choose the graph to fit the data: a bar graph compares exact values of separate categories, a histogram shows data grouped in equal intervals, and a pie chart shows how one whole is shared. Avoid a pie chart with many tiny sectors, because they are hard to compare.
| Data | Best graph |
|---|---|
| exact counts to compare | bar graph |
| numbers in intervals | histogram |
| shares of one whole | pie chart |
Worked examples
A day of 24 hours. The pie shows the angles 120°, 90°, 60°, 30° and 60°. Hours = angle ÷ 360 × 24. Sleep: 120/360 × 24 = 8 h. School: 90/360 × 24 = 6 h. Play: 4 h. Homework: 2 h. Other: 4 h. Check: 8 + 6 + 4 + 2 + 4 = 24.
Shirts. A shop sold 200 shirts, and the pie shows S 20%, M 45%, L 25%, XL 10%. Medium shirts: 45/100 × 200 = 90. Large shirts: 25/100 × 200 = 50. Check: 20% + 45% + 25% + 10% = 100%.
Choosing a graph. The numbers of goals scored by five players: a bar graph, because the categories are separate. The heights of 30 pupils in groups of 10 cm: a histogram. How a 600 LE budget is shared between food, rent and transport: a pie chart.
Class activity
Pie reporter. With a grown-up, find a pie chart in a book or on a poster. Say what the whole is, which sector is biggest and what its percent is. Make up one question that needs the total.
Practice
1
In a pie chart for 50 pupils, a sector has the angle 108°. How many pupils is that?
108/360 × 50 = 15 pupils.
2
What percent of the circle is a sector of 72°?
72/360 × 100 = 20%.
3
In the shirts pie chart, how many large (L) shirts were sold out of 200?
25% of 200 = 50 shirts.
4
Which graph suits the number of goals scored by each of six named players?
A bar graph, because the categories are separate and exact values matter.
5
Salma says a sector of 30% means 30 pupils like football. What is missing?
The total. 30% of 40 pupils is 12, of 100 pupils is 30. We need the total number of pupils.