Year 6 maths · Key Stage 2 · Statistics

Year 6 pie charts, line graphs and the mean: a guide

In Year 6 children read, draw and use pie charts and line graphs to answer questions, and they learn to calculate the mean, an average that shares a total out equally. Pie charts link statistics to fractions, percentages and angles, and line graphs show how something changes continuously, such as temperature over a day or kilometres converted to miles.

Pie charts, line graphs and the mean, explained

A pie chart is a circle divided into slices, called sectors, that show how a whole group is shared between categories. The whole circle is one full turn, which is 360 degrees, so the angle of a sector tells you what fraction of the group it represents. A 90° sector is a quarter, or 25%. A 180° sector is a half, and a 120° sector is a third. If a pie chart shows 40 children and one sector is a quarter of the circle, that sector stands for 10 children. Year 6 children are expected to use this connection between angles, fractions and percentages to find missing amounts.

To draw a pie chart, children first find how many degrees each member of the group is worth by dividing 360 by the total. With 24 children, each is worth 360 ÷ 24 = 15°. They then multiply by the frequency of each category, check that the angles add up to 360°, and draw the sectors one at a time with a protractor, starting from a radius line. Teachers often choose totals that go into 360 neatly, such as 20, 24 or 36, so that the angles come out as whole numbers.

A line graph plots one measurement against another and joins the points with a line. It suits things that change smoothly, like the temperature of a cooling drink or the height of a plant over several weeks, so reading a value between two plotted points gives a sensible estimate. A bar chart is different, because it shows separate categories. Children draw line graphs from their own investigations and from other subjects, and they use conversion graphs. A straight line through (0, 0) can show that about 5 miles is about 8 kilometres, so 40 kilometres is roughly 25 miles. They need to read the scale carefully, because each square on an axis might be worth 2, 5 or 10.

The mean is the type of average found by adding up all the values and dividing by how many values there are. The mean of 12, 15, 9, 20 and 14 minutes of reading is 70 ÷ 5 = 14 minutes. A helpful way to think about it is a fair share: if every child had read for the same time and the total stayed the same, each would have read 14 minutes. The mean doesn’t have to be a whole number or one of the values in the list. Children also use it backwards. If the mean of five numbers is 8, the total must be 40, so if four of the numbers add up to 28 the fifth is 12. They learn to judge when the mean is sensible, for example for test scores or daily rainfall, but not for categories such as favourite colours.

Words your child will hear

Pie chart: A circle divided into sectors to show how a whole is shared between categories.
Sector: One slice of a pie chart. Its angle shows the size of its share.
Frequency: How many times something occurs, such as how many children chose bananas.
Line graph: A graph that joins plotted points with a line, used for measurements that change continuously.
Scale: What each step on an axis is worth. It may count in 1s, 2s, 5s or 10s.
Mean: The total of all the values divided by how many values there are.
Average: A single typical value that represents a set of data. The mean is one type of average.

What the National Curriculum says

In Year 6, pupils should be taught to:

Interpret and construct pie charts and line graphs and use these to solve problems
Calculate and interpret the mean as an average

Objectives from the National Curriculum in England, © Crown copyright, used under the Open Government Licence v3.0.

A worked example

24 children chose their favourite fruit: apples 6, bananas 9, grapes 3 and strawberries 6. Work out the angles to draw a pie chart.

Check the total number of children: 6 + 9 + 3 + 6 = 24. This is the whole circle.
Work out the angle for one child. The whole circle is 360° shared between 24 children.
```
360 ÷ 24 = 15°
```

Multiply the frequency of each fruit by 15°.

Apples      6 × 15 = 90°
Bananas     9 × 15 = 135°
Grapes      3 × 15 = 45°
Strawberries 6 × 15 = 90°

Check that the angles add up to a full turn.
```
90 + 135 + 45 + 90 = 360°
```
Draw a circle and a radius. Measure 90° from the radius with a protractor for apples, then 135° from the new line for bananas, and so on around the circle. Label each sector.
Interpret the chart. Apples have 90°, which is a quarter, so 25% of the children chose apples. Bananas are the biggest sector: 135° out of 360° is 3/8, which matches 9 out of 24 children.

Apples 90°, bananas 135°, grapes 45° and strawberries 90°.

Common mistakes and how to help

Drawing a sector with as many degrees as there are items, such as 6° for 6 children

The frequency is the number on the page, and children don’t think about how it connects to the 360° of the circle.

What helps: Remind them that all the angles must add up to 360°. Ask “what is one person worth?” first, then multiply.

Thinking the mean is the middle number or the one that appears most

Children hear the word “average” used for several different ideas, and the mean, the middle value and the most common value get muddled.

What helps: Explain the mean as a fair share: put everything in one pile, then share it out equally. For 3, 5, 6, 4 and 7 the total is 25, and sharing among 5 gives 5 each.

Dividing by the wrong number when finding the mean

A zero doesn’t look like a value, so children leave it out when they count. If it rained 0, 3, 0 and 5 millimetres on four days, the mean is 8 ÷ 4 = 2 millimetres, not 8 ÷ 2 = 4.

What helps: Count how many values there are, including any zeros, before dividing. Write “total ÷ number of days” under the working.

Misreading the scale on a line graph

Children count each square as 1 when the axis goes up in 2s or 5s, or they read off the nearest labelled line rather than following the grid.

What helps: Before reading anything, work out what one small square is worth. Then use a quick check, such as “half way between 20 and 30 must be 25”.

How to help at home

Survey and slice. Ask 8 family members or friends to choose between three drinks or sports. Cut out a paper circle and fold it in half, then quarters, then eighths, so each person is one eighth, or 45°. Colour the sectors to show the shares and ask what fraction and percentage each choice is.
Weather line graph. Read an outdoor thermometer at the same time every day for a week and plot the readings. Your child can find the mean temperature and talk about the day that was most unusual.
Spot charts in the real world. Pie charts and line graphs appear in news stories, leaflets and sports reports. Ask “which is the biggest slice, and about what fraction is it?” or “what happened between these two points?”.
Fair-share averages. Find the mean number of steps, minutes of reading or pocket-money pounds across a week. Ask whether the answer matches what a typical day looked like.
Miles and kilometres. On a car journey, use 5 miles being about 8 kilometres. If a sign says 10 miles to go, ask roughly how many kilometres that is and how your child worked it out.

Builds on

Year 5: Line graphs, tables and timetables

Leads on to

Key Stage 3: Averages, charts and scatter graphs

Everything in Year 6 maths

Updated 20 October 2026.