Pie charts

In a nutshell

A pie chart shows things as proportions. Everything in a pie chart adds up to $360\degree$ and can be written in degrees, as a fraction or as a percentage.

Interpreting pie charts

Being able to convert between angles and proportions is important when making sense of a pie chart. The following formula can help and your answer can be calculated as a fraction or a percentage:

$\frac{\text{angle}}{360}=\frac{\text{frequency}}{\text{total}}$

Example 1

This pie chart represents the colour of different flowers growing in a field. In total there are $500$ flowers; how many pink flowers are there?

Maths; Statistics; KS4 Year 10; Pie charts

Using the formula:

$\begin {aligned}\frac{54}{360}&=\frac{\text{frequency}}{500} \\\frac{54}{360}&=15\%\end {aligned}$ 

Work out $15\%$ of $500$ :

$10\% + 5\% = 50+25=75$

There are $\underline{75}$ pink flowers.

Drawing a pie chart

Drawing a pie chart involves working out each quantity as a proportion of $360$ and hence an angle.

procedure

1.	Add all the values to find the total represented by the pie chart.
2.	Find the number you multiply the total by to get 360.
3.	Multiply each number by the multiplier to find the angle.
4.	Draw using a protractor and label.

Example 2

Draw a pie chart that represents the different instruments played by students in school.

Instrument	Trumpet	Piano	Guitar	Violin
Number of players	$4$	$20$	$8$	$8$

Find the total number of players:

$4+20+8+8=40$

Find the multiplier:

$360\div40=9$

Multiply every number by $40$ to get the angle:

Instrument	Trumpet	Piano	Guitar	Violin
Angle	$4\times9=36\degree$	$20\times9=180\degree$	$8\times9=72\degree$	$8\times9=72\degree$

Draw and label:

Maths; Statistics; KS4 Year 10; Pie charts