Charts (bar charts, histograms, pie charts, graphs)
3.5 Pie chart principles
Many believe that the prettier a chart, the better it is. But is it? Probably not. The main consideration should be whether the presented chart communicates the information matching the aim. So many examples seen in publications today have multicoloured charts, sometimes in three dimensions and not representing the data effectively to communicate the message contained in them. Sometimes it is appropriate to have more than one colour – but the rationale for the many colours must be understood.
Similarly, the basic principles of each type of chart must be applied – or the resultant chart is unlikely to reflect the data well, making the understanding of the message much more difficult.
For pie charts, the fundamental principle is that the divisions of a pie add to the whole, that is, 100 per cent. The technical term for the individual parts of the pie is segment. The examples used in this section are similar to published examples.
Figure 3.20 Systems evaluation.
Broadly appropriate but
systems need strengthening
29%
Broadly appropriate but disclosure needs
strengthening 18%
Fit for purpose 30%
Not established 6%
Not fit for purpose 12%
For those quick in additions, you will spot that the sum of the percentages given in Figure 3.20 is not 100 but only 95. The title did not have a footnote marker but notes were given under the original. The first note indicated that 5 per cent of the systems had only recently started operating and thus it was ‘too early to judge the strength of
the controls in place’. But the chart has a segment ‘Not established’ so they could not be judged either! A letter was sent to the head of the organisation pointing out the basic principle of a pie chart and the sum of its constituent parts. The response was that they had noted why the 5 per cent were missing. It is actually not any harder to draw a chart where the constituent parts sum only to 95 per cent in Excel – but it would present the user with much more difficulty in understanding the data! Also look at the order of the information: to assist the user in the interpretation of the chart, the order would be better as:
Fit for purpose
Broadly appropriate but system needs strengthening Broadly appropriate but disclosure needs strengthening Not fit for purpose
Only recently started Not established
The other issue here is the use of colour. Only one of the segments was in a different colour – grey – but that would have been more appropriate for the segment ‘Not established’. This chart could be improved by having three colours: green for estab- lished systems that are reasonable, red for the systems that were not fit for purpose and grey for those that could not yet be assessed (those recently started and those not established systems). The result would be Figure 3.21.
Figure 3.21 An improved chart.
Fit for purpose 30%
Broadly appropriate but
systems need strengthening
29%
Broadly appropriate but disclosure needs
strengthening 18%
Not fit for purpose 12%
Only recently started 5%
Not established 6%
CHARTS (BAR CHARTS, HISTOGRAMS, PIE CHARTS, GRAPHS) 53 The next pie chart (Figure 3.22) is an American example measuring recidivism from different offences, that is, the proportion of people convicted of certain offences that reoffend. It is quickly obvious that the basic principle of pie charts has not been observed: the total of the percentages in the segments is 329.1. The data here do not form the division of a whole (100 per cent) and, in fact, should either be shown as five different pie charts (each showing the proportion reoffending and the proportion not reoffending) or the chart needs to be completely rethought and probably drawn as a bar chart! If one chose the five pie charts option, it would be quite difficult to discriminate visually between the relative sizes of the reoffending proportions as they are quite similar.
Figure 3.22 Recidivism in US.
Violent offences 61.7%
Property offences 73.8%
Drug offences 66.7%
Public order offences 62.2%
Other offences 64.7%
Principle 3.6: Ensure the sum of the percentages in a pie chart add to 100.
The aim of the chart is obviously to look at the different rates of recidivism in the prisoners in the United States. The only way such a chart could be used is where each segment of the pie is in proportion to the number of individuals who have reoffended with the rates shown to the side. This, however, would be quite confusing to any reader and would require a significant written description – negating the use of the chart.
So, if the basic aim is to show the different rates of recidivism across the offence groups, a bar chart would be the appropriate type of chart, as in Figure 3.23.
Figure 3.23 Recidivism in US.
0 10 20 30 40 50 60 70 80 90 100
Violent offences Public order offences Other offences Drug offences Property offences
Per cent re-offending
Note that here we have the 0 to 60 common and thus not adding to the story. We could add the average for all types but that would not help much.
Again thinking around the possibilities, we could calculate the average rate of recidi- vism and show the data relative to this figure. To be technically correct, the average should be a weighted average of the percentages but those data were not readily available. So, for illustrative purposes only, the arithmetic average of the percentages has been used as a base figure in Figure 3.24.
Figure 3.24 Recidivism in US.
–10 –5 0 5 10 15
Violent offences Public order offences
Other offences Drug offences Property offences
Difference from average re-offending rate
CHARTS (BAR CHARTS, HISTOGRAMS, PIE CHARTS, GRAPHS) 55 Essentially, Figure 3.24 puts a magnifying glass on the area of Figure 3.23 that is the most interesting. The aim is clearly met and the users can understand that the people committing property offences are much more likely to reoffend than other offence groups.
Principle 3.7: Ensure that a pie chart is the most appropriate type of chart to meet the aim.