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.

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.

Show | Count |
---|---|

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 3^{1}/_{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 |
---|---|

Cars | 140 |

Motorbikes | 70 |

Vans | 55 |

Buses | 5 |

Total vehicles | 270 |

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.

- 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.

- Answer
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.

**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 |
---|---|

11-20 | 9 |

21-30 | 16 |

31-40 | 12 |

41-50 | 4 |

51-60 | 6 |

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:

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.

- Question
How many pupils are between 121-130cm tall?

- 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

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

- Question
What is total number of cars in the survey?

- 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?

- 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.

**Now try a **Test Bite