Bar graphs (bar charts)
A bar graph is a chart that shows data as rectangular bars, one for each category, where the length of each bar shows its value. The categories go along one axis and the values up the other. The bars are all the same width with gaps between them. In the UK, a bar graph is usually called a bar chart.
What is a bar graph?
A class of 40 students was asked how they get to school. The results were walk 14, bus 11, car 9 and bike 6. Here they are as a bar graph:
The height of each bar, read against the scale up the side, is the number of students. You can see at a glance that walking is the most popular and cycling the least, which is the whole point of a bar graph: comparing amounts quickly.
Parts of a bar graph
- Title: says what the data is about.
- Category axis: the groups being compared, each with a label.
- Value axis: the numbers, with a label and units, usually frequency or count.
- Scale: evenly spaced numbers on the value axis, starting at zero.
- Bars: one per category, the same width, with equal gaps.
Types of bar graph
| Type | What it looks like | Use it for |
|---|---|---|
| Vertical (column) bar graph | Bars standing up from the bottom axis | Most data, and the usual choice |
| Horizontal bar graph | Bars running across from the left axis | Long category names, or many categories |
| Grouped (dual) bar graph | Two or more bars side by side in each category | Comparing groups, such as two classes |
| Stacked (composite) bar graph | One bar per category, split into coloured parts | Showing a total and what makes it up |
A grouped or stacked bar graph needs a key (legend) to show which colour is which group.
How to make a bar graph
- Put the data in a frequency table, with a tally if you are counting.
- Draw the axes. Categories along the bottom, values up the side.
- Choose a scale that fits the biggest value and goes up in equal steps from zero.
- Label everything: both axes, every category and the title.
- Draw the bars with a ruler, all the same width, with equal gaps between them.
Choosing a scale
Look at the largest value and pick steps that reach just past it in about 5 to 10 steps. For the school data, the biggest value is 14, so steps of 2 up to 16 work well. If the biggest value were 137, steps of 20 up to 140 would be sensible. Steps of 1, 2, 5, 10, 20, 50 and 100 are easiest to read. US grade 3 students learn to draw scaled bar graphs, where each square stands for more than one, such as 5 pets.
How to read a bar graph
Read along from the top of each bar to the value axis. If a bar stops between two marks, work out what each small division is worth first. Then answer the question with the values you read. Using the school graph:
| Question | Working | Answer |
|---|---|---|
| Which is the most popular? | Tallest bar | Walking |
| How many more walk than cycle? | 14 − 6 | 8 students |
| How many came by car or bus? | 9 + 11 | 20 students |
| What percentage came by bus? | 11 ÷ 40 × 100 | 27.5% |
"How many more" and "how many less" questions like the second one are exactly what US grade 3 students are asked to solve from bar graphs.
Bar graph vs histogram
They look alike but show different kinds of data. A bar graph is for categories, such as types of transport or favourite (favorite in the US) colours. A histogram is for continuous numerical data split into ranges, such as heights from 150 cm to 160 cm.
| Bar graph | Histogram | |
|---|---|---|
| Data | Categories (or separate values) | Continuous data in ranges (classes) |
| Gaps between bars | Yes | No, the bars touch |
| Order of bars | Can be changed | Fixed, along a number line |
| Bar widths | All the same, no meaning | Show the class width, and can differ |
| Vertical axis | Frequency or value | Frequency, or frequency density if widths differ |
In England, AQA's GCSE Maths specification lists bar charts with pie charts and pictograms for categorical data, and histograms, with equal and unequal class widths, for grouped and continuous data. The histogram calculator draws histograms with frequency density.
Bar graph, line graph or pie chart?
- Bar graph: comparing amounts in different categories.
- Line graph: showing how one thing changes over time, such as temperature through a day.
- Pie chart: showing how a whole splits into parts. In a pie chart of the school data, walking would get 14 ÷ 40 × 360 = 126° of the circle.
Misleading bar graphs
The value axis should start at zero. If it doesn't, small differences look huge. Say one product sold 52 thousand and another 48 thousand. On an axis starting at 45, the bars are 7 and 3 units tall, so one looks more than twice the other. Really, 52 is only about 8% more than 48. When you read a graph in the news, check where the axis starts.
Common mistakes
- Uneven scales, such as 0, 5, 10, 20, 50. Every step must be the same size.
- Bars of different widths in a bar graph. Only the length should change.
- No gaps between bars for category data. Touching bars suggest a histogram.
- Missing labels on the axes or the title.
- Misreading small divisions. Work out what one small square is worth before reading a bar.
To practise charts and data among other topics in a short timed paper, try today's Pre-Algebra & Algebra 1 paper. In the UK, the same practice opens as GCSE Maths Foundation.
Common questions
What is a bar graph used for?
Is a bar graph the same as a bar chart?
What is the difference between a bar graph and a histogram?
Why do bar graphs have gaps?
Should a bar graph start at zero?
What is a double bar graph?
Revision cards
Say the answer first, then flip the card to check it.
Where to go next
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Maths · StatisticsLine graph: what it is, how to read and make oneWhat a line graph is, its parts, how to read trends and values from one, how to draw your own, and how it compares with bar graphs, with examples.