Pie charts

Key points

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A pie chart can show collected data in sectors. Each sector can be labelled, or can be colour coded with a key.

A pie chart is a type of graph used to show in a sample of data. A pie chart resembles a circle which has been split into .
The angle of each sector is representative of the proportions of the whole .
If the sectors are coloured, a key should be included to explain what each colour represents.
The proportions in a pie chart may be represented as a .
When drawing a pie chart, a protractor will be used to draw the angles accurately. Being familiar with how to use a protractor will be helpful.

Creating a pie chart

To produce a pie chart, data is required. The data often comes in the form of a table.
To create a pie chart, the size of the angles needed must be calculated.

Add the total frequency in the table.
Divided 360° by the total frequency.
Multiply each frequency by this value. These are the angles for each sector.
Construct a circle and draw a vertical line from the top to the centre.
In a clockwise direction, use a protractor to plot each angle in turn.
Label each sector or use a key to colour code each.
Give your pie chart a title.

Examples

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A student asked their friends how they got to school. The table shows the results. Construct a pie chart to represent the data.
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To construct a pie chart the angles needed must be calculated. First, add the frequencies. In this table the frequencies total 18
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Divide 360° by this value. 360 ÷ 18 = 20°. This means each friend is equivalent to 20° in the pie chart.
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Multiply each frequency by 20 to calculate the angles required. Walk = 8 × 20 = 160. Cycle = 2 × 20 = 40. Car = 5 × 20 = 100. Bus = 3 × 20 = 60. These angles should add up to 360°. If they do not add up to 360°, something is incorrect.
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To plot the pie chart, start by constructing a circle. Use a pair of compasses. Add a vertical line from the centre to the top of the circumference.
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The first sector to be drawn is to represent the friends who walk to school. This angle needs to be drawn at 160°. Position the protractor on top of the circle so that the origin is on the circle’s centre and the zero on the outer degree scale is aligned with the vertical line. Mark the angle at 160°. Remove the protractor and draw a straight line from the centre passing through this point.
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The second sector to be drawn is to represent the friends who cycle to school. This angle needs to be drawn at 40°. Rotate the protractor, keeping the origin on the centre of the circle, and with the zero on the outer degree scale now aligned with the previous line. Mark the angle at 40°. Remove the protractor and draw a straight line from the centre passing through this point.
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The third sector to be drawn is to represent the friends who use a car to travel to school. This angle needs to be drawn at 100°. Again, rotate the protractor , keeping the origin on the centre of the circle and aligning the zero on the outer degree scale with the previous line. Mark the angle at 100°. Remove the protractor and draw a straight line from the centre passing through this point.
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The last sector is the angle that remains. This provides an opportunity to check how accurately the pie chart has been drawn. This angle should be 60°. This can be checked using a protractor.
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All that is left to do is to label the pie chart and give it a title. Each sector can be labelled, or it can be colour coded with a key. An appropriate title for this example would be ‘A pie chart to show mode of transport to school’.

Question

A café owner recorded the type and number of drinks ordered in an hour.The table shows the results. If these were to be represented as a pie chart, what angle would be needed for each sector?

Example. An image of a table. The table has two columns and six rows. The first column is labelled, drink, and is populated with the drinks, tea, coffee, coke, orange, and water. The second column is labelled frequency and is populated with the numbers, three, five, two, one, and one. The cells for the labels are coloured dark grey.

Interpreting a pie chart

It is possible to interpret a pie chart by looking at the proportions of the sectors.
The angles can be used to work out what proportion of the whole population a pie chart sector represents. These fractions would be out of 360°, the number of degrees in a full turn.
A pie chart may include the percentages of what each sector represents. These can also be used to work out proportions of the whole population.

Examples

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$Example one. Using fractions and angles to interpret a pie chart. An image of a pie chart. The pie chart is split into three sectors. The sectors have been coloured, in a clockwise direction, green, blue, and purple. The green sector has an angle of ninety degrees, the blue sector has an angle of two hundred and twenty five degrees, and the purple sector has an angle of forty five degrees. Written right: a key, blue equals win, green equals draw, and purple equals lose. Written above the pie chart: A pie chart to show the outcome of rugby fixtures.$
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The pie chart shows the outcome of results for a rugby team during a season.
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If this pie chart represents 24 fixtures the number of each outcome can be calculated. The sector representing the fixtures that are drawn is one quarter of the fixtures. Games resulting in a draw = 1/4 × 24 = 6 games. Six games resulted in a draw.
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The sector representing the fixtures that are won measures 225°. As a fraction of the whole pie chart this represents 225/360 = 5/8. Games resulting in a win = 5/8 × 24 = 15 games. Fifteen games resulted in a win.
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The pie chart shows the favourite hobby of 660 pupils.
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The sector representing the pupils whose favourite hobby is playing video games is 20% of the pie chart. Number of pupils = 20% of 660 = 0.20 × 660 = 132. One hundred and thirty-two students’ favourite hobby is playing video games.
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The sector representing the pupils whose favourite hobby is playing sport is 45% of the pie chart. Number of pupils = 45% of 660 = 0.45 × 660 = 297. Two hundred and ninety-seven students’ favourite hobby is playing sport.