## What you need to know

A pie chart is a circular chart used to compare the sizes of data sets in relation to one another. The pie is split up into ‘slices’ (sectors is the proper name), and then if one category has more people/things in it than another, then it will get a bigger slice of the pie.

To measure the size of each slice we use the size of the angle that it will take up, out of the total 360\degree of the circle. To calculate the angle, we use the following formula:

\text{angle }=\dfrac{\text{number of things in category}}{\text{total number of things}}\times 360.

Here we’ll see how we can construct a pie chart using this formula, and also how we can use a given pie chart to learn about the information in question.

Example: Brian asks 60 people what their favourite colour is and separates the answers into 5 categories. His results are shown in the table below. Draw a pie chart to display Brian’s results.

To draw the pie chart, we need to calculate the size of the angle needed for each category using the formula shown above.

\text{‘Red’ angle }=\dfrac{10}{60}\times 360=60\degree

\text{‘Blue’ angle }=\dfrac{13}{60}\times 360=78\degree

\text{‘Green’ angle }=\dfrac{24}{60}\times 360=144\degree

\text{‘Yellow’ angle }=\dfrac{5}{60}\times 360=30\degree

\text{‘Other’ angle }=\dfrac{8}{60}\times 360=48\degree

Now we have all the angles, we can draw the chart. Start by drawing a circle with a compass, and then measure the angles with a protractor to make sure we get them right. Finally, give your chart an appropriate title and your result should look like the pie chart shown on the right.

Note: colours are commonly used when constructing pie charts, but they are not necessary. In fact, any pie charts you’ll see in exam questions will have no colours involved, and you won’t be expected to use them.

Example: A survey was done asking 90 people how many bathrooms were in their home. Freddie drew a pie chart to display the results of this survey.

a) What number of bathrooms was most common in this survey?

b) Calculate the number of people who have 1 bathroom in their house.

c) If Freddie picks someone at random from the group surveyed, what is the probability that he chooses a person with exactly 1 bathroom in their home?

a) To answer this, simply look at the pie chart and see which slice is the biggest. Clearly, ‘2 bathrooms’ has the biggest slice, so the most common number of bathrooms is 2.

b) To work out how many people had exactly 1 bathroom in their house, we will have to use a protractor to measure the size of the angle in the ‘1 bathroom’ slice.

We can see that the angle for this sector is 100\degree. Now, we will see two slightly different methods for finding the number of people this represents, but they will both be based on the formula at the top of the page.

Method 1 – We’re trying to find the number of people in a certain category. If we rearrange the initial formula, we get

\text{number of things in category }=\dfrac{\text{angle}}{360}\times \text{ total number of things}

This is now a formula we can use directly to find our answer, given that we know the angle to be 100\degree and we know the total number of people is 90:

\text{number of people with 1 bathroom }=\dfrac{100}{360}\times 90=25

Method 2 – In this method, we want to work out what the ’degrees per person’ value is. We know there are 90 people in total, and we know a circle has 360\degree.

360\div 90=4\text{, therefore } 4\degree \text{ represents } 1\text{ person.}

Now, since there are 100\degree in the ‘1 bathroom’ sector, there must be

100\div 4=25\text{ people with 1 bathroom in their home.}

Note: method 2 works well here because the ‘degrees per person’ value is a nice number, however this may not always be the case. Method 1 will always work regardless.

c) To find the probability of randomly picking someone with 1 bathroom, we just find the proportion of people with 1 bathroom as a fraction of the total. Doing this, we get

\text{probability of picking someone with 1 bathroom }=\dfrac{100}{360}=dfrac{5}{18}

### Example Questions

We need to calculate the size of the angle that we’ll be drawing for each grade. Firstly, calculate the total:

\text{total }=6+5+10+3=24

Then, using the formula, we get

\text{‘A’ angle }=\dfrac{6}{24}\times 360=90\degree

\text{‘B’ angle }=\dfrac{5}{24}\times 360=75\degree

\text{‘C’ angle }=\dfrac{10}{24}\times 360=150\degree

\text{‘D’ angle }=\dfrac{3}{24}\times 360=45\degree

Drawing the circle with a compass, and measuring the angles with a protractor, we get the pie chart shown below.

We will have to measure the angle of the ‘dog’ sector and work out how many pets that corresponds to.

So, the ‘dog’ angle is 125\degree. Using the formula

\text{number of things }=\dfrac{\text{angle}}{360} \times \text{ total},

We get

\text{number of dogs }=\dfrac{125}{360}\times 72 = 25

We could now work out the angle for ‘fish’ and do the same process, or we can just subtract all of our current values from the total:

\text{number of fish }=72-(27+25+8)=12

Thus, the completed table looks like

Firstly, we need to measure the angle of the chocolate slice.

Since we know that this slice constitutes 10 people, we can calculate a ‘degrees per person’ value.

80\div 10=8, \text{ therefore } 8 \degree \text{ represents } 1 person

As there are 360\degree in total, we get that the total number of people in Taylor’s survey is as follows.

\text{total }=360\div 8=45

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