← All lessons
📐 Mathematics - Class 7
Lesson 21 · Statistics

Multiple Bar Diagrams

MathematicsSubject
13 minEstimated read
Length is the only thing the eye compares

The reader is comparing lengths, so the lengths must be in proportion to the numbers.

Drawing a bar diagram

Step What to do
1Draw two axes: categories along the bottom, frequency up the side
2Choose a scale that fits the largest frequency, marked evenly
3Make every bar the same width, with equal gaps
4Label both axes and give the diagram a title
The frequency axis must start at zero

If the axis starts at 950, a bar of 1100 looks three times a bar of 1000. The numbers are correct and the picture is still a lie.

Bars must all be the same width

A wider bar looks more important even when its height is unchanged, because the reader sees the whole area.

Kinds of bar diagram

A double bar diagram puts two related sets side by side and needs a key. Bars can run horizontally when the category names are long.

A bar diagram is not a histogram

Bars with gaps mean separate categories. Bars that touch mean a continuous scale with no gap in it.

Reading a bar diagram

Check the scale, then check where the vertical axis begins. Those two things take ten seconds and prevent almost every wrong conclusion.

🔐

The full lesson is waiting for you

Create a free account to unlock activities, practice tests, presentations and videos - and to track your progress and confidence score for every subject.

Create free accountSign in
Worked Example 1

Favourite sports of 40 students: football 16, cricket 10, volleyball 8, badminton 6.

Choose the scale0 to 20 in steps of 2, starting at zero
Draw the barsFour bars of equal width and equal gaps
Label everythingBoth axes labelled, plus a title
Check against the data16 + 10 + 8 + 6 = 40, matching the students surveyed.
Worked Example 2

Two villages have 1000 and 1100 people, with the axis drawn from 950 to 1150.

What the numbers say1100 ÷ 1000 = 1.1, so ten per cent larger
What the picture saysBar heights of 50 and 150, so the second LOOKS three times the first
Is it a lie?Every printed number is accurate, and the impression is still false.
The fixStart the axis at zero, and the bars differ by a tenth of their length.
🔐

1 more worked examples - sign in to see them all.

Create free accountSign in
Activity 21.2

Draw the same data twice, honestly and dishonestly

What you needSquared paper, a ruler, a pencil and figures that are fairly close together.
Chart oneDraw it properly, with the axis starting at zero and all bars the same width.
Chart twoNow draw the same data to make one bar look dominant, without printing a single wrong number.
Then swapGive both charts to another group and ask them to describe the difference.
🔐

That's a peek at activity 1 of 4 - sign in for all of them, full length.

Create free accountSign in
1

A bar diagram works because the eye judges LENGTH well and numbers badly.

🔐

13 more points to remember - sign in to see the rest.

Create free accountSign in
1Why does a bar diagram show data more clearly than a table does?
2How can a bar chart mislead while every number printed on it is correct?
3What is the difference between a bar diagram and a histogram?
4Why must all the bars in a bar diagram have the same width?
5When would you use a double bar diagram, and what does it need?

Question 1 of 10

1A bar diagram works because people
🔐

Sign in to watch the video for this topic.

Create free accountSign in
Slide 1 of 4
Unit 21 · Bar Diagrams

Bar Diagrams

Mathematics · Grade 7

What You Will Be Able To Do

📊

Draw a bar diagram properly, with scale, labels and equal widths

👥

Use a double bar diagram to compare two related sets

🚧

Tell a bar diagram from a histogram, and why the gaps matter

🔍

Spot a chart that misleads while every printed number is correct

“

A bar diagram works because human beings judge length very well and judge numbers very badly. The reader is comparing lengths, so the lengths must be in proportion to the numbers.

🔐

8 more slides are waiting

Create a free account to watch the full presentation.

Create free account Sign in

Presenter notes: Open with the same forty marks from last lesson, first as a table and then as a bar chart, and ask which one they understood faster. The answer is obvious and it is worth saying why: people compare lengths very well and compare numbers very badly. Then warn them that this strength is also a weakness, because a chart can exploit it, and by the end of the lesson they will know exactly how.