Pie charts and line graphs
Interpret and construct pie charts and line graphs; use these to solve problems
What a learner can do afterwards
- Read values from a line graph showing temperature over a day and identify trends
- Construct a pie chart from given data by calculating sector angles
- Use a pie chart to determine the actual quantity represented by each sector given the total
1 · Read
A line graph shows how something changes over time. Each dot is a value at a certain time, and the dots connect with a line. When the line goes up, the value is increasing. When it goes down, the value is decreasing. When the line is flat, the value is staying the same.
A line graph tracks temperature through a day: 10°C at 6am, 14°C at 9am, 20°C at 12pm, 22°C at 3pm, then 18°C at 6pm. The line rises all morning, keeps climbing into early afternoon, then turns and falls toward evening. The warmest point on the graph is 3pm, right where the line changes direction.
A pie chart shows how a whole amount splits into parts. The whole circle stands for the total, and each slice, called a sector, stands for one part. You already know a full turn is 360°, and that's exactly how much a full circle holds. To find a sector's angle, work out what fraction of the total that part is, then multiply by 360°.
24 children picked a favourite fruit: 12 chose apples, 6 chose bananas, and 6 chose grapes. Apples are 12 out of 24, which is half, so that sector gets half of 360°, which is 180°. Bananas and grapes are each a quarter, so each of those sectors gets 90°.
Once you know a sector's percentage or fraction, you can find the real quantity, too. Just multiply the total by that fraction. If a $40 budget pie chart shows 25% spent on Fun, that's 25% of $40, which is $10.
A line graph shows change over time; a pie chart shows a whole split into parts, each sector sized by its fraction of 360°.
More to read
Data: FAQ
A line graph joins measurements in time order to show change. A temperature graph climbing from 8 degrees at 6am to 18 degrees at 2pm slopes upward all morning. Flat sections mean nothing changed. Reading values means going across from the time, then up to the line, then across to the scale.
42.1: Representing Data Graphically
Bar charts, line graphs and pie charts each suit different questions. Line graphs track change over time, like temperature through a day. Pie charts split one total into shares. A trend question wants lines, a share question wants pie.
2.1 Stem-and-Leaf Graphs (Stemplots), Line Graphs, and Bar Graphs
Pie charts turn shares into angles. A full circle is 360 degrees, so 1/3 of a survey means 120 degrees. With 120 pupils preferring apples out of a survey, the apple sector spans 120 degrees. Angle over 360 always equals share over total. That one equation builds any pie chart.
4 Ways to Make a Pie Chart
A sector also converts back into a headcount. A 90 degree sector of 200 pupils means 90/360 x 200 = 50 pupils. A 60 degree cycling sector in 240 pupils means 40 cyclists. Multiply the total by the angle share. Checking that all sectors add to 360 degrees catches drawing slips.
2 · Watch
Take it off screen
Where it sits
Where this leads
Jobs that lean on this skill. Follow one to see everything it is built on.
17 questions wait behind this lesson, each with its answer explained. Every answer feeds the sky: stars light as they are learned, and dim when it is time to come back.