Maths

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.

Pie charts and frequency diagrams

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.

image: bar graph

In another school, Emmerdale was the most popular soap:

image: bar graph

Remember: the larger the number, the larger the angle in the pie chart.

Pictograms

A pictogram uses symbols to represent frequency.

This pictogram shows the favourite comedy game show from a survey of 60 students.

Favourite comedy game show

ShowCount
Have I Got News for You
Mock The Week
QI
Other

= 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.

Drawing a pie chart

Look at this record of traffic travelling down a particular road.

Traffic Survey 31 January 2008

Type of vehicleNumber of vehicles
Cars140
Motorbikes70
Vans55
Buses5
Total vehicles270

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:

Traffic Survey 31 January 2008

Type of vehicleNumber of vehiclesCalculationDegrees of a circle
Cars140(140/270) x 360= 187
Motorbikes70(70/270) x 360= 93
Vans55(55/270) x 360= 73
Buses5(5/270) x 360= 7

This data is represented on the pie chart below.

image: pie chart

Question

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.

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Answer

 

NewspaperNumber of peopleAngledegrees
The Daily Bugle45(45/90) x 360= 180
England Today20(20/90) x 360= 80
Other15(15/90) x 360= 60
I do not read a paper10(10/90) x 360= 40

This pie chart is drawn stage by stage below.

sequence of a pie chartimage: circle



sequence of a pie chartimage: mark first line at 0 degrees



sequence of a pie chartimage: mark in rest of values



sequence of a pie chartimage: finished pie chart



Before you draw the pie chart, remember to check that the angles which you have calculated add up to 360 degrees.

Drawing a frequency diagram for grouped data

Here is the data for the ages of customers shopping in the Bitesize CD store.

Bitesize CD store 16th May 2008

 
Ages of customers in 1-hour period25, 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:

 

AgeNumber of people
11-209
21-3016
31-4012
41-504
51-606
61+1

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 graphstage 1: draw x and y axis



bar graphstage 2: label the axis



bar graphstage 3: place the correct height of the bars



Interpreting pie charts and frequency diagrams

Example

The pie chart below shows the heights (in cm) of 30 pupils in a class.

image: pie chart

The biggest slice of the pie chart contains the most people - 151-160cm.

Question

How many pupils are between 121-130cm tall?

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Answer

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

Example

A survey was conducted to determine the number of people in cars during rush hour. The results are shown in the frequency diagram below.

image: bar graph

Question

What is total number of cars in the survey?

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Answer

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.

Question

What is the most likely number of people in a car?

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Answer

1.

Cars in the survey are most likely to have 1 person in them as this is the tallest bar - 6 of the cars in the survey had one occupant.

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