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PSLE Mathematics · Primary 5 and 6

Pie Charts and Data Analysis

A pie chart shows how a whole is split into parts, with each part drawn as a sector of a circle. In Primary 6 you read and interpret pie charts and use them to solve problems. Pie charts bring together fractions, percentages, angles and the unitary method, so they are a good test of how well those topics fit together. This guide also covers reading tables, bar graphs and line graphs, which appear in data questions. It ends with a worked example and three practice questions.

What the syllabus expects

  • Read and interpret a pie chart where the sectors are given as fractions, percentages or angles
  • Use the facts that the whole circle represents the whole set of data, 100% and 360°
  • Convert between the angle of a sector, a fraction of the whole and a percentage
  • Find the quantity represented by a sector, and the total from the quantity of one sector
  • Read and interpret data from tables, bar graphs and line graphs
  • Solve problems using information presented in a pie chart

Reading a pie chart

The whole circle stands for the whole set of data, which is 100% of it, and the angle at the centre is 360°. Each sector shows one part. A sector with a right angle at the centre is 90° out of 360°, which is 1/4 or 25% of the whole. A half circle is 180°, 1/2 or 50%. Sectors may be labelled with fractions, percentages or angles, and a question may mix all three. The sectors must add up to the whole, so the fractions add up to 1, the percentages to 100% and the angles to 360°. This fact lets you find a missing sector by subtracting the others from the whole.

Angles, fractions and percentages

To change a sector angle into a fraction, put it over 360° and simplify: 72° gives 72/360 = 1/5, which is 20%. To change a percentage into an angle, multiply 360° by the percentage: 30% of 360° = 108°. A useful link is that 10% of the circle is 36°. To change a fraction into an angle, multiply: 3/8 of 360° = 135°. Once every sector is written in the same form, you can compare them easily. For example, a sector of 90° and a sector of 30% can be compared by writing both as percentages, 25% and 30%, so the second is bigger by 5% of the total.

Finding quantities

To find the quantity in a sector, multiply its fraction or percentage by the total. If 480 pupils were surveyed and a sector is 25%, it represents 25% of 480 = 120 pupils. If you are given the quantity in one sector instead, use the unitary method to find the total. If a 60° sector represents 50 pupils, then 60° is 1/6 of the circle, so the total is 6 × 50 = 300 pupils. To find the difference between two sectors, find the difference in their fractions or percentages first, then take that fraction of the total. Be careful when comparing two pie charts. If the totals are different, a bigger sector does not always mean a bigger quantity.

Tables, bar graphs and line graphs

Data questions also use tables, bar graphs and line graphs. Before reading any values, check the title, the labels on each axis and the scale. If the vertical axis goes up in steps of 5 or 20, work out what each small division stands for before reading a bar that ends between two lines. A line graph shows how a quantity changes, often over time. A steeper line means a faster change, and the biggest increase between two points is where the line rises most steeply. A table may need you to add a row or a column to find a total. Many data questions then ask for an average, a fraction or a percentage of the values you read, so the earlier topics come back here.

Worked example

A pie chart shows how 480 pupils travel to school. 3/8 of them travel by bus, 25% travel by car, the sector for pupils who walk has an angle of 60°, and the rest travel by MRT. How many pupils travel by MRT?

  1. Bus: 3/8 of 480 = 180 pupils.
  2. Car: 25% of 480 = 1/4 of 480 = 120 pupils.
  3. Walk: 60° out of 360° is 60/360 = 1/6, and 1/6 of 480 = 80 pupils.
  4. MRT = 480 − 180 − 120 − 80 = 100 pupils.
  5. Check using fractions: 3/8 + 1/4 + 1/6 = 9/24 + 6/24 + 4/24 = 19/24, so MRT is 5/24 of the pupils, and 5/24 × 480 = 100.

Answer: 100 pupils travel by MRT.

Common mistakes

  • Judging sector sizes by eye. Use only the fractions, percentages or angles given, because pie charts in questions are not always drawn accurately.
  • Treating a percentage as a number of people. A 25% sector is 25% of the total, so multiply by the total to get the count.
  • Forgetting that the angles add up to 360°, not 100. A missing sector angle is 360° minus the others.
  • Comparing sectors from two pie charts with different totals as if the totals were equal. Work out the actual quantities before comparing.
  • Misreading the scale on a bar graph or line graph. Find the value of one small division before reading a bar that ends between two gridlines.
  • Using the wrong total, such as the number of girls when the pie chart shows all the pupils. Check what the whole circle represents.

Exam tips

  • Before calculating, write each sector in the same form, either all as fractions or all as percentages, and check that they add up to the whole.
  • Find the missing sector first. Many questions are built around the one sector that is not labelled.
  • When a question compares two pie charts, write down each total and work in actual quantities.

Practice questions

1. Easy: In a pie chart, one sector has an angle of 108°. What percentage of the whole does it represent?

Show answer

30%. Working: 108/360 = 3/10 = 30%.

2. Medium: A pie chart shows how a family spends $2400 each month. 35% is spent on food, 1/5 on transport and the rest is saved. How much more is saved than spent on transport?

Show answer

$600. Working: food = 35% of $2400 = $840. Transport = 1/5 of $2400 = $480. Savings = $2400 − $840 − $480 = $1080. Difference = $1080 − $480 = $600.

3. Harder: School A has 1200 pupils and its pie chart shows that 30% like football best. School B has 900 pupils and its pie chart shows that 40% like football best. Which school has more pupils who like football best, and by how many?

Show answer

Neither, both have 360. Working: School A has 30% of 1200 = 360 pupils and School B has 40% of 900 = 360 pupils. The bigger sector in School B does not mean more pupils, because School B has fewer pupils altogether.

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