Construct & interpret column graphs
Theory
Constructing and interpreting column graphs is a Year 3 data skill: reading and building a column graph (bar graph) that has a title, labelled axes and an even scale. This page shows how to read the height of a column on a scale of \(1\)s or \(2\)s, compare groups, find totals and differences, and draw columns from a table. Curriculum: VC2M3ST02 / AC9M3ST02.
A column graph (also called a bar graph) shows data as upright columns. Each column stands for a group, and the height of the column shows how many are in that group. Taller means more.
Every good column graph has the same parts. It has a title that says what it is about, and two labelled axes. The bottom axis names the groups, and the side axis is a number scale. The scale is even, going up in equal steps such as \(1\)s or \(2\)s, and it always starts at \(0\).
To keep the graph fair, the columns are equal in width with equal gaps between them. Only the height changes. To read a value, follow the top of a column across to the scale. To interpret a graph means to read it and answer questions; to construct one means to draw the columns from a table of numbers.
A column graph is not built from formulas, but every one should have these parts. Use this checklist when you read or draw a graph.
- Title — says what the graph shows and who it is about.
- Labelled axes — the bottom axis names the groups (categories); the side axis is the number scale.
- Even scale from 0 — equal steps such as \(1\)s or \(2\)s, always starting at \(0\).
- Equal columns — same width, equal gaps; only the height changes.
When the scale goes up in \(2\)s, each mark is worth \(2\). Multiply the number of marks by the step to find a value, and divide by the step to find how many marks tall to draw a column:
How to read a column graph
- Read the title and axes. Find out what the graph is about and what each axis shows.
- Check the scale. Look at the steps on the side axis. Is each mark worth \(1\), \(2\) or something else?
- Find the group. Look along the bottom axis for the column you want.
- Read the height. Follow the top of that column straight across to the scale and read the number. If it stops between two marks, find the number halfway.
How to construct a column graph
- Draw and label the axes. Put the groups along the bottom and a number scale up the side, starting at \(0\).
- Choose an even scale. Go up in equal steps that reach your largest number.
- Draw each column. Make every column the same width with equal gaps, and draw it up to the right height (amount \(\div\) step marks).
- Add a title. Write a title that says what the graph shows and who it is about.
| \(\text{each mark}\) | \(=\) | \(2\) |
| \(\text{cat} \to 3\text{ marks}\) | \(=\) | \(3\times2 = 6\) |
\(6\) students own a cat.
| \(\text{dog}\) | \(=\) | \(10\) |
| \(\text{bird}\) | \(=\) | \(2\) |
| \(10 - 2\) | \(=\) | \(8\) |
\(8\) more students own a dog.
| \(\text{each mark}\) | \(=\) | \(2\) |
| \(14 \div 2\) | \(=\) | \(7\) |
The column should be \(7\) marks tall.
| \(10 + 6\) | \(=\) | \(16\) |
| \(16 + 4 + 2\) | \(=\) | \(22\) |
Add every column height: there are \(22\) pets.
| \(\text{halfway between 10 and 12}\) | \(=\) | \(11\) |
The marks go up by \(2\), so halfway is \(1\) more than \(10\). The column shows \(11\).
| Lunch | Pasta | Sushi | Salad | Wrap |
|---|---|---|---|---|
| Students | 6 | 2 | 3 | 8 |
Draw the axes, label the bottom axis "Lunch" and the side axis "Number of students", and mark a scale in \(1\)s from \(0\) to \(8\). Draw each column the same width with equal gaps, up to its number.
| \(\text{pasta}\) | \(=\) | \(6\text{ marks}\) |
| \(\text{wrap}\) | \(=\) | \(8\text{ marks (tallest)}\) |
The wrap column is the tallest. A good title says what and who: "Favourite lunch of class 3P".
Common pitfalls
Frequently asked questions
What is a column graph?
A column graph, also called a bar graph, shows data as upright columns. Each column stands for a group, and the height of the column shows how many are in that group.
How do you read a value from a column graph?
Find the group on the bottom axis, then follow the top of its column straight across to the number scale on the side. The number it lines up with is the value.
What are the parts of a column graph?
A column graph has a title, two labelled axes, an even number scale that starts at zero, and equal-width columns with equal gaps between them.
How do you read a column that stops between two marks?
Find the number halfway between the two marks. On a scale of \(2\)s, a column halfway between \(14\) and \(16\) shows \(15\).
How do you find how many more one column has than another?
Read the height of each column, then subtract the smaller height from the larger. For example, \(8 - 3 = 5\), so the taller column has \(5\) more.
Does the width of a column matter?
No. Only the height of a column shows how many. All columns are drawn the same width, so the width never changes the count.