Pie Charts

A pie chart is a circle split into slices called sectors. Each sector stands for one category, such as one way of getting to school. The bigger the sector, the bigger the share of the whole group in that category.

The size of a sector is its angle at the centre of the circle. The whole circle is 360^\circ, so the whole group is always 360^\circ. Half the group is 180^\circ and a quarter is 90^\circ, which is shown with a right-angle mark.

The frequency of a category is how many are in it. A frequency is not an angle: 20 people does not mean a 20^\circ sector. You always have to share out the 360^\circ between the whole group.

In the exam you may be asked to draw an accurate pie chart from a table, usually for 3 marks. You may also be asked to read a pie chart: find the mode, find what fraction of the group is in a sector, work out how many people a sector stands for, or work out how many people there were altogether. Some questions give two pie charts and ask you to compare them, for 1 to 4 marks.

First add up the frequencies to find the total. Then share 360^\circ between everyone: each person gets 360 \div \text{total} degrees. Multiply by the frequency to get the sector angle.

You can also write it as one calculation:

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

The fraction is the category's share of the whole group, and the angle is the same share of 360^\circ.

If you are given a percentage, use 10\% = 36^\circ, because 10\% of 360 is 36. So 25\% of a group is 90^\circ.

• Work out every angle and write them down, in a column next to the table if there is space.
• Check that the angles add up to 360^\circ.
• Draw the first angle from the line already drawn from the centre, with a protractor.
• Draw each next angle from the line you have just drawn.
• Label every sector with its category name.

Put the centre of the protractor exactly on the centre of the circle, and line up its zero with the line you are measuring from. Examiners allow you to be up to 2^\circ out on each angle.

The labels must be the category names, such as Bus or Walk. Writing only the angle, such as 120^\circ, in a sector does not count as a label. Show your angle calculations too: they can earn marks even if your drawing is a little out.

The mode is the category with the biggest sector. Write down the category name, not the angle.

The fraction of the group in a sector is \frac{\text{angle}}{360}. For example, a 120^\circ sector is \frac{120}{360} = \frac{1}{3} of the group. A right angle is \frac{1}{4}.

To find how many people a sector stands for, you need the total. Work out how many degrees each person gets, 360 \div \text{total}, then divide the sector angle by it. Or work out the fraction of the total.

A probability from a pie chart is a fraction of the whole group. For a sector, it is \frac{\text{angle}}{360}. For a number of people, it is \frac{\text{number}}{\text{total}}. Never put a number of people over 360.

Sometimes you know the angle and the frequency for one sector, but not the total. Work out what fraction of 360^\circ the sector is. The frequency is the same fraction of the total.

Another way is to find the degrees for one person: angle \div frequency. Then the total is 360 \div the degrees for one person.

Once you know the degrees for one person, you can find the number in any other sector too. Never add or take away angles and people in the same calculation: they are different things.

A pie chart shows proportions: what share of its own group is in each category. Two pie charts can show groups of different sizes, even when the circles are the same size.

So a bigger angle shows a bigger proportion, but not always more people. To compare numbers of people, work out the number in each chart using that chart's own total.

If the totals are not given, you cannot say which group has more people in a category. You can only compare the proportions.

• Using the frequencies as the angles. Share 360^\circ between the whole group first, then multiply by each frequency.
• Labelling sectors with angles only. Write the category name in each sector.
• Not showing the angle calculations. Write down every angle you work out, and check they add up to 360^\circ.
• Giving the angle as the mode. The mode is the name of the category with the biggest sector.
• Mixing up angles and people. Turn angles into people with the degrees for one person; never add or take away a mix of the two.
• Comparing angles when the totals are different. Work out the actual numbers in each chart before you say which group has more.