Representing Data: Tables, Charts and Diagrams

The data decides the diagram

Almost everybody chooses a chart the wrong way round. They decide what they want the finished thing to look like, or they use whatever the software offered first, and then they force the data into it. The decision actually runs the other way, and it can be made before anything is drawn at all. What was measured or counted decides what can honestly be shown, because each diagram carries one particular kind of meaning and simply cannot carry the others. A bar chart compares the sizes of separate groups, and the gaps between the bars exist because the groups are separate. A pie chart shows how a whole divides into parts, which means it is only ever truthful when the parts really do make up a whole and nothing overlaps. A line graph joins points because something continuous is changing between them, which is why joining unrelated categories with a line is nonsense however tidy it looks. A scatter graph puts two measurements from the same thing against each other, which is the only way to show whether they move together. So the skill this module builds is a decision rather than a drawing: look at what you actually have, and work out which diagram can carry it. What each diagram is called and how it is drawn is covered elsewhere on this course, as is how to judge a claim somebody else has made with statistics.

Five words for choosing

These name what a diagram is FOR. Get these right and most choices make themselves.

Which diagram can carry it?

Why not a pie chart?

A survey asks people which of six sports they play, and lets them tick as many as they like. Somebody presents the results as a pie chart. What is wrong with that?

• People could tick more than one, so the parts overlap and do not make a whole
• Six categories is too many for a pie chart to be readable
• Bar charts are always better than pie charts
• Nothing is wrong, since the data is in categories

Two charts that look alike

Bar charts and pie charts are both used for categories, which is why they get swapped for each other. They answer different questions.

Choose a diagram in this order

Five steps for deciding how to represent a set of data. Put them in the order that makes the choice obvious.

• Say what was actually counted or measured, and on what
• Decide what kind of data that makes it
• Decide what question the diagram is meant to answer
• Choose the diagram that can carry that kind of data and that question
• Check the choice does not claim something the data does not support

When a pie chart is honest

Which THREE conditions have to hold before a pie chart tells the truth?

• Each thing counted falls into exactly one category
• The categories between them cover everything that was counted
• The total is meaningful, so a share of it means something
• There are no more than four categories
• The categories are roughly equal in size

Drawable is not the same as defensible

Every piece of software will draw whatever you ask it to. Hand it a column of numbers and it will produce a pie chart, a line graph, a stacked bar and half a dozen things with shadows on, and not one of them will warn you that the data cannot support what you have just made. That is the modern version of this topic, and it is why the checking has to happen in your head before the software is opened. Three cases come up again and again. A pie chart of a survey that let people tick more than one answer, where the slices add to more than everything and the circle is simply false. A line graph joining separate categories, where the line implies that there are meaningful values BETWEEN favourite sports, which there are not. And a chart built from a total that means nothing, where a share of it means nothing either. None of these is a drawing mistake. Each one is a claim the data does not support, dressed up in a picture, and in an exam the mark comes from being able to say WHICH claim is being made and why it fails. So when you meet a diagram, in a question or in the wild, ask what it is asserting about the data rather than whether it looks neat. And when you make one, decide what the data can carry before you decide what you would like to see.

Complete the representing sentences

A separate group that something either belongs to or does not is _____. Measurements that can take any value in a range are _____. Two measurements taken from the same person or object are _____. A set of parts that together account for everything exactly once is _____.

Work out the sector

A pie chart shows how 240 people travelled to work. Sixty of them walked. Work out the angle of the sector for walking, in degrees.

One survey, three diagrams

A class collects three different things in one week, and each needs a different diagram for reasons that have nothing to do with taste. First, they ask everybody which one subject they would most like an extra lesson in. That produces separate categories, each person in exactly one, and the categories cover everybody who answered. Either a bar chart or a pie chart is honest here, and which you choose depends on the question: a bar chart if you want to compare the subjects, a pie chart if you want to show how the class divides up. Second, they count how many people are in the library at each hour from nine until four. That is something changing over time, and the hours between the readings are real, so a line graph is right and the joining lines mean something. A bar chart would work but throws away the sense of a trend. Third, they measure both the time each person spent on homework and the mark they got. That is two measurements from each person, which is paired data, and only a scatter graph can show whether the two move together. Notice that none of the three decisions needed anybody to look at a chart. Each was settled by saying what had been measured and on what, which is the whole point.

Find the diagram that lies

Five statements about diagrams a group has made. Tap the ONE where the diagram claims something the data cannot support.

• We used a bar chart for how many people chose each of the five options.
• We used a line graph for the number of visitors recorded each hour through the day.
• We used a pie chart for a question where people could tick as many options as applied to them.
• We used a scatter graph for the height and the shoe size we measured from each person.
• We used a bar chart rather than a pie chart because we wanted to compare the groups.

Justify the choice

A choice of diagram earns marks when it names what the data is. Choose the option in each gap.

The representing run

Five quick decisions about diagrams. Three lives.

Three sets of results

A group has finished collecting data for a project and has to present three different findings. You are advising them on how to show each one. Work through three decisions.

• They asked one hundred people which single mode of transport they used to get to school. What do you advise?
• They also asked which after-school clubs people attend, letting them name as many as they wanted. What do you advise?
• They measured how long each person spent travelling and how far they lived from school. What do you advise?

Explain the choice

A group surveyed one hundred people and asked which of six leisure activities they take part in, letting people name as many as apply. They plan to show the results as a pie chart. Explain why that is the wrong choice and what they should do instead.

• Say what a pie chart claims about the data it shows
• Explain exactly why allowing several answers breaks that claim
• Name the diagram they should use instead, and say what it shows
• Explain what question their chosen diagram would answer
• Finish with the general rule this case illustrates