skip to page contents Diagrams and Charts


Note - this topic contains specialised formatting and symbols. If you copy parts of it to the Scratch Pad this formatting may be lost. You can print the guidance without losing the formatting and symbols. There are 11 pages.

Why use diagrams and/or charts?

Although presenting tables of numbers can be very informative, they can lack visual impact. You may want the user to see the message instantly. A diagram, chart or graph can help by summarising the key features of the data, and representing it as a picture.

This topic looks only at diagrams and charts. For help with using graphs to illustrate your work see the sub topic ‘Graphs’ beneath the title for this topic or in the menu to the left of the screen.

For help with interpreting diagrams and charts see the sub topic 'Interpreting Data' beneath the title for this topic or in the menu to the left of the screen.

You can scroll down to read all the help in this topic or click on one of the links below to go straight to a specific area.

What type of diagram or chart to use?
There are many different types of diagram and chart. To help decide which best suits your needs, each of the following is looked at in detail below:


It may also help you decide which to use if you consider the difference between discrete and continuous data.

Once you have chosen the type of diagram or chart you want to use, you will need to decide:

Bar chart

A bar chart is the most common type of diagram, and is frequently used.

 

 

 

.bar chart showing number of cars sold against colour of car

It represents data in terms of bars of equal width, whose height varies to represent the size of the data. Also note that the bars can be any width, and sometimes may be just thin vertical line.
When to use a bar chart:

A bar chart is particularly useful when one or two categories 'dominate' results. In the diagram above, it is clear that red cars are the most popular.

  • It can be very clear and easy to read.
  • Most people understand what is presented without having to have detailed statistical knowledge.
  • It can represent data expressed as actual numbers, percentages and frequencies.
  • A bar chart can represent either discrete or continuous data.
  • If the data is discrete there should be a gap between the bars (as in the diagram above).
  • If the data is continuous there should be no gap between the bars.

Histogram

A histogram looks similar to a bar chart, but in this case the area of the bar or rectangle varies with the data, rather than just the length.

 

histogram showing number of people on holiday against age of people

When to use a histogram:
  • It can only be used to represent continuous data.
  • It can represent data expressed as actual numbers, percentages and frequencies.
  • It is really only of value if the reader gets more information from a chart where the classes are different sizes.

Pictogram

A pictogram uses pictures or symbols to represent a number of units of data. The pictures usually relate to the data shown.

 

 

pictogram showing the number of pets against type of pet

When to use a pictogram:
  • These can be some of the most visually appealing diagrams to use.
  • They are often used as part of advertising campaigns.
  • Make sure that it is appropriate for your needs, don’t let the medium get in the way of the message. It can be tempting to use pretty pictures but these may make the information less clear; they may also trivialise the topic.
  • It is not always suitable for large quantities of data. You do not necessarily need one picture per piece of data (in the diagram above, one picture represents two pets). However, you may still need to show smaller quantities (eg half a picture represents one pet) and it may be hard to read if divided further.
  • Some pictograms can vary the size of the symbols rather than the number. Do not use this, unless you are confident. It should be the area of the picture that increases in proportion to the frequencies rather than the length, otherwise this can be misleading.

Pie chart

 

 

A pie chart shows data in terms of proportions of a whole. The 'pie' is divided into segments that represent this proportion. This is done by dividing the angles at the centre.

Favourite Sport Group of the First Year Students

pie chart showing percentages of favourite sports amongst first year students

For help with how to draw a pie chart by hand see the end of this section.

When to use a pie chart:
  • It is best used to present the proportions of a sample.
  • It is most useful where one or two results dominate the findings.
  • It can represent data expressed as actual numbers or percentages.
  • Do not use where there are a large number of categories, or where each has a small, fairly equal share, as this can be unclear.

Scattergram

A scattergram shows how two sets of numerical data relate to each other.

 

scattergram

When to use a scattergram:

These are used to show patterns of correlation between two sets of data - ie how 'connected' the data is. Eg there is likely to be a connection between height and shoe size but there is not a connection between height and eye colour.

Each point represents one relationship (eg one person’s height and shoe size). A 'line of best fit' can be inserted to show a trend (see above).

Stem and leaf plot

This displays the actual data as well as its frequency. This uses part of the data as the class or group heading, this is called the stem. The remainder of the value is listed in the bars, ie. the leaf.

 

 

stem and leaf plot

When to use a stem and leaf plot.
  • As all the actual values are shown, this type of diagram is only really appropriate for small quantities of data
  • This type of diagram is unique in that you can see the raw data as well as the frequency in it - ie in the diagram above, you can see that 4 of the first-time mothers are in their thirties (4 is the frequency) and you can also see that their ages are 32, 32, 34, 36 (this is the raw data). As such, you or your reader may be able to extract it later and perform further analysis.
  • It is not used very often as its appearance can be offputting.

Producing diagrams and charts using IT or by hand

IT - produced diagrams and charts (using spreadsheet packages).

These are useful if you wish to include a diagram within a report.

Advantages:  
  • professional presentation
  • wide variety of presentation styles can be used
  • aimed specifically for use within projects, could be the right tool for the job
  • simple to use with step-by-step guidance.
Disadvantages:
  • Because they are intended for presentation use they may not always be accurate - they are intended to be representations.
  • Without gridlines it can be very difficult to read the results.
  • The software makes a number of assumptions about layout that may not be how you intended to present your data.
  • If you have chosen to produce a pictogram to present your data you will have to use a draw facility rather than a chart wizard. This may be time consuming and you may not be able to use the symbols or pictures that you would have liked.

For more help with producing diagrams and charts using IT, see 'IT Skills' in the menu to the left of the screen.

Hand-drawn diagrams and charts.

NB When producing a diagram or chart by hand always:

  • use a sharp pencil
  • use a ruler to draw the axis and the 'bars'
  • make use of colour where possible.
Advantages:
  • You have complete control over the appearance of the diagram.
Disadvantages:
  • May not be as visually pleasing as a computer-produced diagram.
  • If you are producing a pie chart by hand you will need to be comfortable with using a protractor. If the data you want to present is in terms of percentages, you may find a pie scale useful. This looks like a 360° protractor, but the circle is divided into 100 parts.

Presenting your information

Whether you choose to produce a diagram or chart by hand or by computer, you will need to make decisions about how best to present your information.

What to consider:
  • Who is the user of the diagram?
  • What are you trying to communicate within it?
A diagram or chart makes an immediate visual impact.

It should be clear to the user what you are trying to say:

  • Give it an appropriate and informative title.
  • Label your axes when appropriate.
  • Show sources of data if not stated elsewhere.
  • If your diagram shows results of a sample that represents a population give the sample sizes.
  • Number your diagrams within a piece of work along with other tables, graphs and illustrations. This will make it easier for the user to follow and help you when referring to it within the body of the text.
Other considerations.

The size of the diagram produced within a report can affect the quality of the information contained within it - don't make it too small.

There are a large number of different diagrams and charts available within IT packages. Some of these are in 3 dimensions. These may look very appealing but do they convey the information you want them to? Don’t let the medium get in the way of the message. Get a friend to look at your diagram or chart and check that they get your message.

Don't overuse diagrams as this may detract from the message. If your key diagram follows a number of less important ones, will the user recognise its importance, or even look at it at all?

How to draw a pie chart by hand

Activity - Follow the steps to produce a pie chart by hand.

 

When producing a pie chart it is important that these are constructed accurately. The 'pie' is divided with regard to the angles at the centre of the circle. There are 360° in total. These must be divided in proportion to the data.

Example.
A sample of 30 students were asked how many brothers and sisters they had. Results were as follows:

student sample results table

Use the steps listed below to produce a pie chart to display this data.

Step 1:
Put the data into a table and convert the actual numbers into degrees.

Complete the following table:

No. of siblings
No. of students
Conversion
No. of degrees
0
4
1
12
2
8
3
3
4
2
more
1
 
30
 

To convert the number of students into degrees:

Result for class x 360
Total in sample

The number of degrees should always be rounded to a whole number.

The total number of degrees must always equal 360° (check, especially if you have had to round any of the answers).

You now know how to divide the degrees at the centre of the 'pie'.

Step 2:
Draw the circle, using compasses.

Always mark your page with a dot first and then use this as the centre of you circle. It can be very difficult to find the centre after the circle has been drawn.

diagram of a circle

Step 3:
Draw a line from the centre to the top of the circle. This will be your starting point for plotting your results.

diagram of a circle with a line drawn from the centre to the top of the circle

Step 4:
Mark the first portion of the 'pie'.

Put the protractor on the line, with + at centre of circle and 0 towards its edge.

Follow the protractor numbers round from 0 to 48° and mark. Draw a line at this point from the centre of the circle to the edge.

dargram of a circle marked with a sector

Step 5:
Repeat this for each of the other results.
Put the protractor on the new line you have just drawn (at 48°), again with + at centre of circle and 0 towards the edge of the circle.

Follow the protractor numbers round from 0 to 144° and mark. Draw a line at this point from the centre of the circle to the edge.

Continue with the other results. Take care to always move your protractor to the new line you have just drawn.

Step 6:
Add colour, an informative title and key.

Your pie chart should look something like this:

pie chart showing the percentage number of siblings per student

What does it tell you? For more help with interpreting pie charts see the sub topic ‘Interpreting data' beneath the title for this topic or in the menu to the left of the screen.

Discrete and continuous data.

Discrete data is....

data which can only be of certain definite values (eg shoes sizes can only have definite values, say 5, 51/2, 6 etc and there are no values between these). Discrete data can be a number of categories as well as number classes (eg car colours).

Continuous data is..... data which can take any value within a particular range (eg measurements).
Why do we need to know?

When choosing the most appropriate type of chart to use, it is important to understand the difference between discrete and continuous data.

To test if data is discrete or continuous, ask yourself: "Is it sensible to have a value between two of the actual results?"
If yes, then the data is continuous (eg if two heights are given as 1.5 m and 1.6 m, yes there can be a height between them).
If no, then it is discrete (eg if part of the data is for two years, 1997 and 1998, there cannot be an entry between them; likewise if the data shows two types of pet say - cats and dogs, it is not sensible to have an category between them).

Written by Louise Thorpe, Learning and Teaching Institute, Sheffield Hallam University
Courseware designed by Mark Briggs, Centre for Multimedia in Education, Sheffield Hallam University

© LTI, Sheffield Hallam University, 2000
This information is for the use of students enrolled on SHU courses only.