Construct column graphs
Theory
To construct a column graph, draw one bar for each category with its height set by the frequency. Start the scale at \(0\), rise in equal steps, and keep the columns the same width with equal gaps.
A column graph shows data as upright bars, one bar for each category.
The height of a column is the frequency read from the table, so a taller column means a larger count.
The columns are all the same width with an equal gap between them, because the categories are separate groups.
The vertical scale starts at \(0\) and rises in equal steps; a title and axis labels say what the graph shows.
Plan the axes before drawing the bars.
- Put the categories along the horizontal axis, evenly spaced.
- Choose a scale for the vertical axis that reaches the largest frequency.
- Mark the scale in equal steps, starting at \(0\).
- Draw each column up to its frequency, keeping every width and gap the same.
How to construct a column graph
- Draw the axes and start the vertical scale at \(0\).
- Scale the axis in equal steps up to the largest frequency.
- Plot a column for each category with height equal to its frequency.
- Label both axes and give the graph a title.
The height equals the frequency.
| Tuesday | \(=\) | \(7\) |
The tallest column is the largest frequency.
| \(9>6>5>4\) | Wednesday |
Add every column.
| \(6+4+9+5\) | \(=\) | \(24\) |
Count the steps up to \(20\).
| \(20\div4\) | \(=\) | \(5\) |
Mark \(4, 8, 12, 16, 20\).
Common pitfalls
Frequently asked questions
How tall should each column be?
As tall as its frequency. Read the count for the category from the table and draw the column up to that number on the scale.
Why must the scale start at zero?
So that heights can be compared fairly. When the scale starts at \(0\), a column twice as tall really does stand for twice as many.
Why are there gaps between the columns?
Because the categories are separate groups, not one continuous measurement. The bars are kept apart, all the same width, with equal gaps.
How do I choose the scale?
Pick a step so the largest frequency fits, then mark equal steps from \(0\). For a largest value of \(20\), steps of \(4\) give marks at \(4, 8, 12, 16, 20\).
What labels does a column graph need?
A title saying what the graph is about, and a label on each axis. The vertical label names what is counted and its unit.