Resources For Teachers For Tutors For Students & Parents Pricing
Primary - Stage 3 (Year 5 & 6) Stage 3 (Year 5 & 6) Data

Construct column graphs

20 practice questions 0 video lessons Theory + worked examples
Create a free accountTrack your progress and save your work as you go.
Create free account

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.

Column graph built from a table A column graph with a vertical scale from 0 to 8 rising in twos. Columns for Monday 4, Tuesday 7, Wednesday 3 and Thursday 6, all the same width with equal gaps. 02468 Cans collected MonTueWedThu
Each column's height is the frequency from the table (Mon \(4\), Tue \(7\), Wed \(3\), Thu \(6\)). The scale starts at \(0\) and rises in equal steps.

Plan the axes before drawing the bars.

  1. Put the categories along the horizontal axis, evenly spaced.
  2. Choose a scale for the vertical axis that reaches the largest frequency.
  3. Mark the scale in equal steps, starting at \(0\).
  4. Draw each column up to its frequency, keeping every width and gap the same.
Only the heights should differ. Equal widths and equal gaps keep the comparison fair.

How to construct a column graph

  1. Draw the axes and start the vertical scale at \(0\).
  2. Scale the axis in equal steps up to the largest frequency.
  3. Plot a column for each category with height equal to its frequency.
  4. Label both axes and give the graph a title.
Example 1 — Column height
A table gives Tuesday \(=7\). How tall must the Tuesday column be?
Solution

The height equals the frequency.

Tuesday\(=\)\(7\)
Example 2 — Tallest column
Cans collected are Mon \(6\), Tue \(4\), Wed \(9\), Thu \(5\). Which day has the tallest column?
Solution

The tallest column is the largest frequency.

\(9>6>5>4\)Wednesday
Example 3 — Total
The four columns are \(6,\ 4,\ 9,\ 5\). How many cans altogether?
Solution

Add every column.

\(6+4+9+5\)\(=\)\(24\)
Example 4 — Choose a scale
The largest frequency is \(20\). A scale rising in steps of \(4\) needs how many marks above \(0\)?
Solution

Count the steps up to \(20\).

\(20\div4\)\(=\)\(5\)

Mark \(4, 8, 12, 16, 20\).

Common pitfalls

Start the scale at zero. If the axis starts higher, a column twice as tall no longer means twice as many.
Equal width, equal gaps. Only the heights should differ, so keep every bar and every gap the same size.
Label everything. A title and axis labels tell the reader what the columns count and in what units.

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.