Bar charts and pie charts

The graph for categories

A bar chart has one bar for each category. The height of a bar is its frequency. There are gaps between the bars, because the categories are separate things.

Try it in Python

The pie chart

A pie chart is a circle cut into slices. It shows how a whole is shared. Each slice has an angle:

For cricket: $\dfrac{18}{40} \times 360^\circ = 162^\circ$. For football: $\dfrac{10}{40} \times 360^\circ = 90^\circ$. For hockey and chess: $54^\circ$ each. The angles add up to $162^\circ + 90^\circ + 54^\circ + 54^\circ = 360^\circ$, which is a good check.

You should find that the three angles always add up to $360^\circ$. Raising one count makes the other two slices smaller, even though their counts stay the same.

Bar or pie?

• To compare the categories with each other, use a bar chart. It is easy to see which bar is taller.
• To show the share of each category in the whole, use a pie chart. But slices that are nearly equal are hard to compare.

What makes a good chart?

• A title that says what the chart shows.
• Labels on the axes, with the unit.
• Bars that start at zero. If the axis starts higher, a small difference looks very large.
• Bars in a sensible order: from the tallest to the shortest, or in the natural order of the categories.
• Not too many slices in a pie chart. With more than five or six slices, a bar chart is clearer.

Practise with new numbers

Common mistakes

• Using a pie chart for data that is not parts of a whole. The slices must add up to the whole.
• Cutting off the bottom of the bars. The height must stand for the value from zero.
• Joining the bars of a bar chart. Gaps show that the categories are separate. Touching bars belong to a histogram.
• Forgetting the title and the labels. Without them, nobody can tell what the chart shows.

Remember these

• A bar chart has one bar for each category, with gaps.
• A pie chart: the angle of a slice is its share of 360 degrees.
• Give a chart a title, label its axes, and start its bars at zero.

Check yourself

Try each one on your own first. If you are stuck, open a hint. Then check with Show the answer.

1. What is the angle of a slice that is $25\%$ of the whole?

2. Do the bars of a bar chart touch?

3. A class has 12 students who walk, 8 who cycle and 20 who come by bus. What is the angle of the bus slice?

4. Why can a bar chart whose axis starts at 90, not 0, mislead the reader?