Graphical Presentation Of Tabular Data - Pie And Doughnut Charts (part 5 Of 5)

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This is the fifth and final article in a series aimed at showing the benefits of presenting tabular data in a graphical format; this one considers the use of pie and doughnut charts. It looks at when they should be used, how they are constructed and the benefits that they can provide.

The Pie Chart

This is a graphical representation chart, which is circular in format. It is named a pie chart because it resembles a pie which has been cut into slices. The pie represents the whole or 100% of the survey sample and each of the slices into which the pie is subdivided, which make up the whole pie, illustrate the quantity proportion of the pie that each element of the survey represents.

This simple statistical chart can be very colourful, as each slice can be drawn as a different colour to ease identification. They are also very easy to produce. Pie charts enable the viewer to easily compare both the individual sizes of different slices of the pie and each slice's proportion of the whole pie or sample. However, it is not always easy to compare slices across two or more pie charts or where many of the elements of a sample are very small when compared with the largest element, because their representative slices are very thin.

Using the child's height survey example which has been used throughout this series of articles, a pie chart can be constructed thus:

Height Range(m.) / Frequency(No.) / Percent(%) /Central Angle(degrees)
1.0m.-1.1m. / 0No. / 0% / 0.0degrees
1.1m.-1.2m. / 1No. / 4% / 14.4degrees
1.2m.-1.3m. / 4No. / 16% / 57.6degrees
1.3m.-1.4m. / 9No. / 36% / 129.6degrees
1.4m.-1.5m. / 7No. / 28% / 100.8degrees
1.5m.-1.6m. / 3No. / 12% / 43.2degrees
1.6m.-1.7m. / 1No. / 4% / 14.4degrees
1.7m.-1.8m. / 0No. / 0% / 0.0degrees
Survey Totals 25No. / 100% / 360 degrees

To generate a pie chart for the above set of data, you have to extend the original table. For each of the height range frequencies it is necessary to calculate the percentage of a full pie chart's circle that that element's slice will be represented by and hence its central angle. For example, using the 1.2m to 1.3m height range above, the frequency percentage is calculated by dividing the frequency 4 by the survey sample size 25 and multiplying by 100, which equals 16 per cent. The central angle of the 1.2m to 1.3m range pie slice is then calculated by multiplying that slice's percentage 16 by 360 and dividing the result by 100 which equates to 57.6 degrees. A short cut to this answer is to multiply the frequency (4) by 360 and divide by the total survey sample size (25) which omits the percentage stage of the calculation.

When all the pie chart's frequency central angles have been calculated, then a pie chart can be generated by drawing a circle of a diameter best suiting the surveyor. Each height range frequency is then represented by a slice with their respective central angle. When all the slices have been drawn, they will make up a full circle of 360 degrees and may be given a different infill colour for improved presentation and identification.

The Doughnut Chart

The doughnut chart is very similar to the pie chart, the difference being that instead of the chart being a solid circle representing a 'pie', the chart is in the form of a hollow doughnut. The calculation for each slice of the doughnut is exactly the same as the pie chart. The main difference is in the graphical representation of the chart in that the doughnut can be given either a two or three dimensional visual representation by using both internal and external edge shading to the doughnut figure. It is also possible to pull a slice of the doughnut in or out in order to emphasise a particular slice.

This is the fifth and final article, introducing the reader to simple graphical presentation of tabular data. Many spreadsheet software packages now include programmes to generate many or all of the graphs and charts highlighted within these articles. It is therefore always a good idea, and indeed good practice, to try to display your survey data in as many different chart and graph formats as possible. You may then determine and choose which ones both best demonstrate what your survey is about, and what your conclusions are; and also which are the easiest for your audience to view and interpret.
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Paul E West has 1 articles online

Paul West works for Education City, an educational software specialist who offers a range of e-learning tools perfect for KS1 teaching. These include fun games for kids and maths resources for teachers.