11.5 Pie Charts

You may have heard of Florence Nightingale as a pioneer in nursing practice, but did you know how important data was to her and that she also invented the pie chart?

Videoclip iconThis brief video will give you an insight into her work:

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Although bar charts are useful to display numbers and percentages, sometimes you may wish to stress how different components contribute to the whole. Pie charts are often used where you want to compare different proportions in the data set. The area of each slice (or sector) of the pie represents the proportion in that particular category.

For example, the pie chart below illustrates the favorite type of exercise for a group of people.

This pie chart shows the percentages for each category, so you can read these off directly. The most popular activity was walking (40%), followed by cycling (24%) and swimming (18%).

Notice, however, that the source of the data has not been stated, so you do not know where it came from or how many people were interviewed. It is important to consider both these points. If, for example, it was a small sample, you may not wish to rely on the results to generalize to a larger group.

Sometimes the percentages are not marked on the chart. So, the proportions can then be roughly estimated by eye. For example, the pie chart below illustrates how employees in a particular company travel to work.

Solution symbolActivity: How Employees Travel to Work

Use the pie chart above to answer the following questions.

(a) Do more people travel to work by bus or by train?

Solution symbol

Answer

(a) The slice of the pie representing bus travel is larger than the slice representing train travel, so yes, more people travel by bus than by train.

(b) Would it be correct to say that the number of employees who travel to work as car drivers is about twice the number who travel as car passengers?

Solution symbol

Answer

(b) The slice of the pie representing car drivers is about twice the size of the slice representing car passengers, so it is correct to say that the number of employees who travel to work as car drivers is about twice the number who travel as car passengers.

(c) Estimate the proportion of employees who travel to work by car, either as the driver or as a passenger.

Solution symbol

Answer

(c) The two slices for car drivers and passengers cover about two-thirds of the circle, so about two-thirds of employees travel to work by car, either as the driver or as a passenger.

It is important to remember that pie charts are useful only for comparing proportions, looking at parts of a whole. If you are interested in other aspects such as trends or frequencies, then other graphs or charts may be more appropriate.

If necessary—provided the pie chart has been drawn accurately—you can also work out the percentages by measuring the angle at the center of the pie for each sector, using a protractor.

For example, the angle at the center of the circle for the “Car Passenger” category is about 80º.

Because a complete circle measures 360º, the fraction that this sector represents is 80 postfix degree divided by 360 postfix degree almost equals 0.22, or 22%.

So about 22% of the employees travel to work as car passengers.

Pie charts are often used to give an overall impression rather than detailed information, so on many occasions a rough estimate will suffice.

Solution symbolOptional Activity: How Employees Travel to Work

If you have a protractor you can print off the pie chart and work out the proportions for the other sectors.

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Comment

You may need to extend the lines of the circles for each sector so that you can measure them properly with the protractor.  Line up the bottom 0° line with one side of the sector and make sure that the center of the protractor is on the center of the circle.

Check your measurements add up to 360°.

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Answer

The angles measured from the pie chart are:

Passengers in cars79°
Bus43°
Train26°
Cycle13°
Walk30°
Other
Car162°

Calculation of percentages

Passengers in cars79°21.9% (to 1 d.p.)
Bus43°11.9% (to 1 d.p.)
Train26°7.2% (to 1 d.p.)
Cycle13°3.6% (to 1 d.p.)
Walk30°8.3% (to 1 d.p.)
Other1.9% (to 1 d.p.)
Car162°45% (to 1 d.p.)

You may have noticed that the total percentage does not add up to 100%; this is due to rounding all the values to 1 d.p.

For the calculation of the percentages it would be better in you can to include the workings.

Don’t worry if you didn’t get exactly the same values—there are bound to be some small differences in the measurement of the angles which will affect this.

For more practice interpreting pie charts, try the following lesson:

11.4.3 Comparative Bar Charts

11.6 Reading and Drawing Graphs and Charts—A Summary