# 2.2.2 Reading graphs and charts: manipulating numbers

Text is just one way of communicating information. Numbers are another way, but whether presented singly, in groups or even as tables , numbers often require a lot of work from the reader to uncover the message. A much more immediate and powerful way to present numerical information is to use graphs and charts. When you use single numbers or tables, the reader has to visualise the meaning of the numbers. Graphs and charts allow the reader to do this at a glance. To show how powerful these representations can be, look at a bar chart created from the numbers in Table 1 (Figure 11).

## Table 1 Percentage of total notified salmonella food poisoning incidents caused by different species in selected years

Year | Salmonella typhimurium |
Salmonella enteritidis |
Other types of salmonella |
---|---|---|---|

1981 | 38.9 | 10.7 | 50.4 |

1983 | 51.4 | 11.7 | 36.9 |

1985 | 41.1 | 23.2 | 35.7 |

1987 | 37.3 | 33.4 | 29.3 |

1989 | 24.3 | 52.6 | 23.1 |

1991 | 19.3 | 63.0 | 17.7 |

1993 | 15.6 | 66.1 | 18.3 |

The bar chart in Figure 11 shows three bars for the first year, one bar for the percentage of food poisoning incidents caused by each of the two named types of salmonella bacteria, plus one bar for all the other types of salmonella lumped together. After a gap, there are three bars for the next year, then another three for the third year, and so on for each of the seven years selected. This type of bar chart is used to compare different sets of data and is called a *comparative bar chart*.

## Activity 6

Compare the numbers in the two representations to convince yourself that the bar chart is the data from the table presented in a different way.

### Discussion

Look at the top row of numbers in Table 1. Find the figure 38.9 per cent – which is the percentage of salmonella-related food poisoning incidents in 1981 caused by *Salmonella typhimurium*. If you ‘round’ this figure to the nearest whole number, it comes to 39 per cent. Now look at the top of the left-hand bar in Figure 11. Again, the figure is 39 per cent – so this vertical bar stands for the percentage of food poisoning incidents due to *Salmonella typhimurium* in 1981. The key at the top of the chart tells you this. Now check the first figure in the next column of Table 1. It shows a 10.7 per cent level of food poisoning incidents. This rounds to 11. On top of the second bar in Figure 11 you will see 11. Quickly check all the numbers in the table to convince yourself that they are the same as the numbers in the chart. Make sure you agree that the key at the top of the chart agrees with the headings in the table.

Now look at the table and see if you can detect any clear patterns. Then look at the chart, scanning from left to right and back again, trying to detect patterns. I hope you agree that the trends show up more clearly in the chart than in the table. You can see that the percentage of *Salmonella enteritidis* cases has risen steadily from a very low level to a very high level, whereas the percentage of incidents caused by *Salmonella typhimurium* has gradually decreased (as has the percentage of incidents caused by all other types of salmonella). This shows us what we have already learned from the table – that there have been consistent trends in the numbers of cases of certain food poisoning organisms. But the diagram brings out the message much more clearly and forcefully. This is one of the reasons for presenting data in diagrams rather than in tables. If you choose the right kind of diagram, it makes the *patterns* in the data very much clearer. Incidentally, when dealing with percentages, it often helps to draw a *percentage bar chart*, in which the bars are stacked on top of one another to make 100 per cent. This emphasises that you are dealing with proportions of a total rather than actual numbers.

In fact, the bar chart is not the only type of diagram we can use to display this type of data. We can also use a line graph (see Figure 12).

## Activity 7

Once again, try cross-checking some of the numbers from Table 1 to Figure 12, to convince yourself that we are indeed looking at the same data presented in a different way.

For instance, does 66.1 per cent for the incidence of *Salmonella enteritidis* in 1993 occur in Figure 11, Figure 12 and Table 1?

### Discussion

If anything, the trends show up even more clearly in the line graph than in the bar chart. For example, you can see the steady rise in the proportion of *Salmonella enteritidis* incidents from 1981 at the left of the graph to 1993 at the right of the graph. And the ‘blip’ in the *Salmonella typhimurium* figure for 1983 is much more obvious. Indeed, the line graph is so clear and direct that you might well ask why anyone would bother with a bar chart.

The reasons for preferring a bar chart are, first, that it is not quite so abstract as the line graph, and second, that it represents the type of data involved better. When you see solid bars representing the food poisoning incidents in each year, it reminds you that the chart represents lots of real cases of people suffering. In fact, the bar chart gives you a better picture of the *overall quantity* of incidents in each year. That information is there in the line graph too, but it doesn't show up so clearly. With the line graph, the figures are condensed to a set of points, so you have to work a little harder to remind yourself of what the diagram is telling you. In addition, the numbers in Table 1 are discontinuous data for specific years, and so do not include all possible 12-month periods over the time covered. Although drawing lines to join up the points helps us to see trends, the lines do not represent points or years in-between.

## Counting and measuring things

How numbers are used in graphs and charts depends on what the numbers are to represent.

Some things occur in a *discrete* way; the quantities change by one (or more) whole units at a time. You can't have three and a quarter eggs in a box; you have to have three or four. While the statisticians' ‘average family’ may contain 1.7 children, real families contain 0,1,2,3, … or more. Quantities that occur in a discrete way – the number of children in a family, the number of eggs in a box, or the weekly output of a car factory – can all be *counted*.

Other quantities occur in a *continuous* way. These quantities can change by amounts as small as (or smaller than) you can imagine. Examples include a person's weight or height, the amount of water in a tank, the temperature of that water, the amount of time spent on a journey, and so on. These quantities have to be *measured*.