Pie charts and frequency diagrams
Once you have collected your raw data, you need to represent it in a diagram. Two ways of doing this are to use a pie chart or frequency diagram.
In a survey, 100 school students were asked to name their favourite soap opera. The results are shown in a pie chart and a frequency diagram below.
In another school, Emmerdale was the most popular soap:
Remember: the larger the number, the larger the angle in the pie chart.
A pictogram uses symbols to represent frequency.
This pictogram shows the favourite comedy game show from a survey of 60 students.
|Have I Got News for You|
|Mock The Week|
= 4 people
For the show Have I Got News for You, 3 smiley faces mean this is the favourite for 12 students, as 3 x 4 = 12.
For QI there are 31/2 smiley faces. 1/2 is equal to 2 students, so in total 14 students rate QI as their favourite.
Look at this record of traffic travelling down a particular road.
|Type of vehicle||Number of vehicles|
To draw a pie chart, we need to represent each part of the data as a proportion of 360, because there are 360 degrees in a circle.
For example, if 55 out of 270 vehicles are vans, we will represent this on the circle as a segment with an angle of: (55/270) x 360 = 73 degrees.
This will give the following results:
|Type of vehicle||Number of vehicles||Calculation||Degrees of a circle|
|Cars||140||(140/270) x 360||= 187|
|Motorbikes||70||(70/270) x 360||= 93|
|Vans||55||(55/270) x 360||= 73|
|Buses||5||(5/270) x 360||= 7|
This data is represented on the pie chart below.
Ninety people were asked which newspaper they read.
45 read the Daily Bugle.
20 read England Today.
15 read another paper.
10 do not read a paper.
Calculate the number of degrees required to represent each answer in a pie chart.
|Newspaper||Number of people||Angle||degrees|
|The Daily Bugle||45||(45/90) x 360||= 180|
|England Today||20||(20/90) x 360||= 80|
|Other||15||(15/90) x 360||= 60|
|I do not read a paper||10||(10/90) x 360||= 40|
This pie chart is drawn stage by stage below.sequence of a pie chart
Before you draw the pie chart, remember to check that the angles which you have calculated add up to 360 degrees.
Here is the data for the ages of customers shopping in the Bitesize CD store.
|Ages of customers in 1-hour period||25, 29, 45, 19, 36, 17, 60, 51, 39, 24, 15, 13, 31, 18, 24, 32, 37, 27, 23, 53, 41, 34, 29, 28, 52, 17, 55, 47, 34, 28, 22, 20, 64, 39, 38, 33, 24, 16, 27, 19, 26, 27, 25, 32, 26, 48, 54, 35|
We could show this data in a bar chart, but it would have a lot of bars! As ages are continuous data, we can group them together so that we have fewer categories.
This is the same set of data put into groups:
|Age||Number of people|
We can now put the data into a pie chart or frequency diagram.
When choosing intervals for the data sets make sure that they do not overlap and that they include all the data.
For example you could use the above intervals to draw a frequency bar chart:bar graph
The pie chart below shows the heights (in cm) of 30 pupils in a class.
The biggest slice of the pie chart contains the most people - 151-160cm.
How many pupils are between 121-130cm tall?
The angle of this section is 36 degrees. The question says there are 30 pupils in the class. So the number of pupils of height 121 - 130 cm is:
36/360 x 30 = 3
A survey was conducted to determine the number of people in cars during rush hour. The results are shown in the frequency diagram below.
What is total number of cars in the survey?
6 + 3 + 5 + 1 = 15
There are 6 cars with one person in, 3 cars with two people, 5 cars with three people, and 1 car with four people.