Construct column graphs
Theory
A column graph shows categorical data as columns. Every column graph needs a title, axis labels and a scale that starts at \(0\) and goes up in equal steps. This Year 5 maths page shows how to choose a scale and draw each column to the right height.
The title tells the reader what the graph is about. The horizontal axis shows the categories; the vertical axis shows the frequency.
The scale must start at \(0\) and go up in equal steps (such as \(1\)s, \(2\)s, \(5\)s or \(10\)s). It must reach at least the largest frequency.
Choose the step so the scale has about \(5\) to \(10\) marks: largest value \(12\) suits steps of \(2\); largest value \(37\) suits steps of \(5\) up to \(40\).
Columns are the same width with gaps between them, because each category is a separate group.
If a value falls between two marks, the top of the column goes between them: \(7\) on a scale of \(2\)s is halfway between \(6\) and \(8\).
A checklist for a column graph:
| Part | What to check |
|---|---|
| Title | Says what the graph is about |
| Axis labels | Name the categories and what is counted |
| Scale | Starts at \(0\), equal steps, reaches the largest value |
| Columns | Same width, with gaps, correct heights |
Drawing a column graph
- Find the largest frequency and choose a scale step.
- Draw the axes and mark the scale from \(0\) in equal steps.
- Draw one column per category, the same width with gaps.
- Add a title and label both axes.
Thursday is \(7\), halfway between \(6\) and \(8\).
(i) \(0\) to \(20\) in \(2\)s
(ii) \(0\) to \(40\) in \(5\)s
(iii) \(10\) to \(40\) in \(5\)s
The second scale. The first is too short and the third does not start at \(0\).
(i) How many bottles were collected in all?
(ii) How much taller is the Wednesday column than the Tuesday column?
| \(9 + 5 + 12 + 7\) | \(=\) | \(33\) |
| \(12 - 5\) | \(=\) | \(7\) |
(i) \(33\) bottles
(ii) \(7\) bottles taller
| \(96 - (33 + 21 + 25)\) | \(=\) | \(17\) |
\(17\), between the \(15\) and \(20\) marks.
\(60\), the first multiple of \(10\) that is at least \(58\).
The biggest value is \(12\). Steps of \(2\) reach \(12\) in only \(6\) steps, so the scale is short and easy to read.
The step from \(6\) to \(10\) is \(4\), not \(2\). The scale should be \(0, 2, 4, 6, 8, 10, 12\).
Common pitfalls
Frequently asked questions
Where should the scale start?
At \(0\).
How do I choose the scale?
Look at the largest value and pick a step (\(1\), \(2\), \(5\), \(10\)) so there are about \(5\) to \(10\) marks.
What does the title tell you?
What the graph is about.
What if a value is between two marks?
Draw the top of the column between them, e.g. \(9\) halfway between \(8\) and \(10\).
Why are there gaps between columns?
Each column is a separate category.