- Sections:
- 0, Chapter 1, Introduction,
### Introduction

This unit continues the topics of data collection and data presentation and illustrates different ways in which you can present data.

You will become familiar with bar charts, pie charts, line graphs and histograms.After completing this unit you should understand how to construct and

- present data clearly in the form of pictograms and charts.
- use pie charts to illustrate discrete data
- use line graphs to illustrate data
- use stem and leaf plots to illustrate numerical data
- use histograms with equal class intervals to illustrate continuous data.

There are five sections in this Unit, namely:

- Pictograms and Bar Charts
- Pie Charts
- Line Graphs
- Stem and Leaf Plots
- Frequency Graphs: Histograms

- 0, Chapter 2, Data Presentation: Bar Charts,
### Data Presentation: Bar Charts

Here is some data for Manchester City, the winners of the Premier League in the 2018/19 season.

The table below gives their scoring record in their \(38\) matches (20 teams in the Premier League;

each team plays every other team, at home and away).What does this data show?

Overall Manchester City are good at scoring goals!

How can we illustrate this data to show its meaning?

We can make some progress by analysing the data using a tally table to show the frequency of each

number of goals scored in the 38 games played - 1, Chapter 2.1, Tally Table,
### Tally Table

In a tally table each data item is shown as a vertical line (I).

After four data items, the fifth is indicated by a line drawn through the previous \(4\) and a space left before starting the next set of lines.

For example the entry IIII III shows a frequency of \(5 + 3 = 8\)

- 1, Chapter 2.2, Bar Chart,
### Bar Chart

Here is a bar chart to illustrate the frequency of goals scored by Manchester City in the 2018/19 Premier League.

- 1, Chapter 2.3, Horizontal Bar Chart,
### Horizontal Bar Chart

Here is another bar chart but this has been turned round.

- 1, Chapter 2.4, Pictogram: Example,
### Pictogram: Example

There are many other ways to display data; the aim is for someone to look at the display and have a good idea of what it is showing.

Here is a different type of data. The table below gives the number and colour of cars sold by a garage over a month.How can this data be illustrated?

A pictograms is one possible way of showing this data.

- 1, Chapter 2.5, Pictogram to Illustrate Data,
### Pictogram to Illustrate Data

Here one car picture represents exactly \(1\) car.

Sometimes it might represent more if the numbers were much larger.

You have to look at the ‘key’ to the pictogram.

- 1, Chapter 2.5, Task 1, Exercise 1,
### Exercise

**Exercise 1**The pictogram shows how many suitcases were sold by a store from 2013 to 2019, with one row missing.

- How many cases were sold in 2014?

\(400\) - What is the smallest number of cases sold in a year?

\(250\) - What is the greatest number of cases sold in a year?

\(700\) - In 2018 a total of 550 cases were sold.

How many suitcase symbols should be there?

\(5\frac{1}{2}\)

**Exercise 2**The bar chart below shows the shoe sizes of a group of 15-year-old boys.

- How many boys are there in the group?

Answer: \(23\) - Comment on the shape of the bar chart, saying whether or not this is the shape you would expect.

Answer: We would expect there to be many more boys with shoe sizes around \(8\) and \(9\) than \(5\) or \(12\), so the results are surprising.

- How many cases were sold in 2014?
- 0, Chapter 3, Data Presentation: Pie Charts,
### Data Presentation: Pie Charts

We will use our colour of cars data from the first section as an example.

To construct a pie chart, the angles around the circle must be in proportion to the number of cars of each colour.

It is the**AREA**that represents the size of the data.

There are 24 cars in total and 360° around the circle, so each car is represented by angle: 360° ÷ 24 = 15°

There are 8 White cars so the angle for White cars is \(8\times15^\circ = 120^\circ\).We calculate the angles for each colour in the same way as in the table.

See the result in the next section.

- 1, Chapter 3.1, Pie Chart for Colour of Cars,
### Pie Chart for Colour of Cars

Using the angles calculated, here is the pie chart

This is a straightforward way of illustrating qualitative data (that is, the colour of cars); we will next look at how to illustrate quantitative data. - 1, Chapter 3.1, Task 1, Exercise 2,
### Exercise

**Exercise**This pie chart, not drawn to scale, shows the Saturday morning activities of a group of 120 children.

- The sector for soccer is represented by an angle of 150°.

How many children play soccer on Saturday mornings?

\(Number =\frac{150}{360}\times\) - Given that 46 children swim on Saturday mornings,

calculate the value of \(x\).

Angle \(x=\frac{46}{120}\times 360^\circ=138^\circ\)

- The sector for soccer is represented by an angle of 150°.
- 0, Chapter 4, Data Presentation: Line Graphs,
**Data Presentation: Line Graphs**Here is another way to illustrate the Manchester City goals-scored data.

We have joined up the data points but does this make sense?

Not really as you cannot score 21\(\frac{1}{2}\) goals in a game; it does though show overall trends.

Line graphs are useful though in showing continuous data, for example temperature or length or weight.

- 1, Chapter 4.1, Illustrating Continuos Data,
### Illustrating Continuos Data

Here is the average monthly temperature at Chichester.

A line graph does make sense here as the data trend can be seen; that is, increasing from Feb to Aug and then decreasing until the end of the year.

- 1, Chapter 4.1, Task 1, Worked Example 1,
### Worked Examples

- 1, Chapter 4.1, Task 2, Worked Example 2,
### Worked Examples

- 0, Chapter 5, Stem and Leaf Plots,
### Stem and Leaf Plots

Here is another very simple way which quickly gives an overall view of the general characteristics of the data.

This is called a stem and leaf plot and here how it works. - 1, Chapter 5.1, Times for One Mile,
### Times for One Mile

Use the slider to explore worked examples.

- 1, Chapter 5.1, Task 1, Exercise 3,
### Exercise

**Exercise**Blood samples were taken from \(40\) blood donors and the lead concentration (mg per \(100\;ml\)) recorded.

- Construct a stem and leaf plot to represent the data.
- What are the values of the range and the median (middle) value?

a.

b.

\(Range = 65 – 17 = 48\;and\;median = 30\)

- 0, Chapter 6, Frequency Graphs: Histograms,
### Frequency Graphs: Histograms

For continuous data, when any value over a range of values is possible, a frequency graph like the one below can be used to illustrate the data.

This is called a histogram, and is characterised by having a continuous scale along the horizontal axis.

Care must be taken about the end points.For example, the interval (in mins) would normally be \(30 \leq \times \lt 35\), so that a time of \(35\;minutes\) would be in the second interval.

- 1, Chapter 6.1, Using the Histogram,
### Using the Histogram

- 1, Chapter 6.1, Task 1, Worked Example 3,
### Worked Examples

- 1, Chapter 6.1, Task 2, Exercise 4,
### Exercise

**Exercise**This histogram shows the weights of learners in a school.

- How many had a weight greater than \(70\;kg\)?

\(5\) - How many had a weight between \(50\) and \(65\;kg\)?

\(55\) - How many had a weight less than \(50\;kg\)?

\(15\) - How many learners were there in the school?

\(81\)

- How many had a weight greater than \(70\;kg\)?
- 0, Chapter 7, Summary,
### Summary

- 0, Chapter 1, Introduction,
- Interactive Exercises:
- Data Presentation Interactive Exercises, https://www.cimt.org.uk/sif/datascience/ds3/interactive.htm
- Pictograms and Bar Charts, https://www.cimt.org.uk/sif/datascience/ds3/interactive/s1.html
- Pie Charts, https://www.cimt.org.uk/sif/datascience/ds3/interactive/s2.html
- Line Graphs , https://www.cimt.org.uk/sif/datascience/ds3/interactive/s3.html
- Stem and Leaf Plots, https://www.cimt.org.uk/sif/datascience/ds3/interactive/s4.html
- Frequency Graphs: Histograms, https://www.cimt.org.uk/sif/datascience/ds3/interactive/s5.html

- YouTube URL: https://youtu.be/I0hq39GamQU

- File Attachments: media/course-resources/Data-Presentation_Learning-Objectives.pdfmedia/course-resources/Data-Presentation_PowerPoint-Presentation.pptxmedia/course-resources/Data-Presentation_Text.pdfmedia/course-resources/Data-Presentation_Answers.pdfmedia/course-resources/Data-Presentation_Essential-Information.pdf