Graphs and charts
GRAPHS AND CHARTS
Graphs and charts It is often easier to get a point across visually than by presenting people with a mass of figures. Graphs and charts are useful for: .
summarizing data
.
detecting trends over time
.
searching for patterns among large amounts of data
.
analysing relationships between variables.
It is often not possible to see any kind of pattern in a mass of raw data, but drawing a graph – even a rough-and-ready one simply for your own purposes – can be the best way to tease out the salient points, and to identify trends or areas of concern. Once these have been identified, you may have to undertake further analysis of the figures before you can reach a decision. The easiest way to draw graphs and charts is to enter your figures into a computer spreadsheet and let it do the work for you. There are now many spreadsheet and graphics software packages that can produce a wide variety of graphs and charts. This has made the production of high-quality material much easier than it used to be and has thereby transformed the exchange of graphical information.
Bar charts In its simplest form a bar chart consists of a number of separate bars whose heights correspond to the sizes of each of the groups being illustrated. An example is shown in Figure 1. 12000 Number of notifications
10000 8000 6000 4000 2000 0
1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997
Figure 1 Notifications of food poisoning in Scotland, 1982–96 (Source: Scottish Executive website, 1999)
Activity What information does Figure 1 give you?
The numbers of notifications of food poisoning were fairly steady from 1982 to 1994, but rose rapidly from 1995. What you cannot tell from this graph is whether an increasing number of people are getting food poisoning or whether more people are contacting their CROWN COPYRIGHT ª 2004
13
MANAGING INFORMATION
doctors; increased publicity could be a contributory factor to the large increases in the last three years. The scale on the vertical axis allows you to estimate the number of cases in any given year to the nearest thousand, but you wouldn’t be able to ascertain the exact number of reports from this graph. The purpose of the graph is simply to give an overall impression of the incidence of food poisoning. Component, or stacked, bar charts A more complicated type of bar chart is the component bar chart or stacked bar chart, which allows an extra dimension of the data to be shown. The sizes of the various components that make up a bar are illustrated using different colours or types of shading and the components are always stacked in the same order. The components of the bars that represent the same item are shaded or coloured in the same way so that they can be easily compared. Have a look at the data in Table 1. A good way to examine any patterns that emerge from the data would be to draw a stacked bar chart. One thing to keep in mind is that there is usually considerable flexibility about the way graphs and charts are presented: it’s very much a creative process. By drawing some graphs for yourself, you will get a feel for some of the choices involved, and this will make you more aware of how people can, for instance, choose their scales to present their figures in the most favourable light. Table 1 Maternities with multiple births (Source: Office of Population, Censuses and Surveys, Birth Statistics 1998) Age of mother
Maternities with multiple births 1978
1988
1998
5,930
7,622
9,080
327
337
303
20–24
1,494
1,689
1,078
25–29
2,231
2,714
2,457
30–34
1,393
1,966
3,332
485
916
1,910
All ages Under 20
35 and over
Let’s consider how we might present a component bar chart using the data in Table 1. It is easier to draw a chart on graph paper than on ordinary paper because the graph paper has a grid. The first thing to do is to decide how you want your graph to look. With a component bar chart you can choose which element of the table to use as ‘classes’ – i.e. the bars – and which as the ‘components’ of the bars. In this case, for instance, you could use either the age ranges as the classes and the years as the components within each bar or vice versa. This is where creativity comes in, but it should also be tempered with an awareness of what message you want to get across. If you use the ages as the classes, your chart will show how the total number of multiple births varies across women of different ages, with a breakdown within each bar of how many of these occurred in each of the three years. If the years are used as
14
CROWN COPYRIGHT ª 2004
GRAPHS AND CHARTS
the classes, you will have a chart showing the total number of multiple births in each year, with a breakdown of the ages of the mothers who gave birth within each of the three years. For this exercise, we’ll choose the latter arrangement. The next stage – which is often the hardest part – is to choose suitable scales for the axes of your graph. The aim is to make the graph as large and clear as possible within the available space. (It’s preferable to work in pencil until you are absolutely sure that you’ve got everything right.) Fortunately, the horizontal axis does not pose much of a problem in this case as we have only three classes of data – the years – so an appropriate scale might be to make the bars 2 cm wide with 1 cm gaps between the bars. The bars need to be labelled at their centres with the class labels, in this case the years. Now let’s consider the vertical axis. With a component bar chart, the heights of the bars represent the total number of items in each class so the scale chosen needs to take account of this. Table 1 already shows the class totals, so you do not have to calculate them. The largest total is 9,080. A suitable scale would be 1 cm to 1,000 births. To make the graph easier to read, you could label the vertical axis ‘Number of births (000s)’ so that the numbers against the tick marks on the axis would be 1, 2, 3 and so on; a tick mark is the small dash made against the axis to divide up the scale. The completed axes would look like Figure 2. ,+ 5
L7.b&4 1' b*46)5 #+++5$
4 3 2 1 0 / . , +
Figure 2
,534
,544 X&a4
,554
Axes for a bar chart
Now you need to draw the bars. It is best to draw the full bar first and then to divide it into the components. With this scale it will not be possible to draw the bars to a greater accuracy than about the nearest 100 (1 mm). After the bars have been drawn, the next stage is CROWN COPYRIGHT ª 2004
15
MANAGING INFORMATION
to divide each bar; the components should always be stacked in the same order in each bar. The easiest way to work out the size of the components is to put your ruler against the scale on the vertical axis and to read off the measurement required for a strip of this size. For the first component of the first bar, the strip height needs to represent 327 women. By finding the value 327 (or 300) on the scale, you can then read off the required length of the strip from the scale on the ruler. In this case it would need to be about 3 mm long.
Activity Draw the bars and components on the labelled axes in Figure 2.
Your component bar chart is nearly complete. All you need to do now is to add a title, a note of the source of the data, and a legend or key to explain the meaning of the different components. The title could be something like ‘Maternities with multiple births: ages of mothers’ – this is written above or below the chart. Table 1 gives the source of the data, which you should write at the bottom of the chart so that anyone can refer back to the original source if they require the precise figures, which cannot be determined from the chart. I&< T0%&4 .+
Graphs and charts It is often easier to get a point across visually than by presenting people with a mass of figures. Graphs and charts are useful for: .
summarizing data
.
detecting trends over time
.
searching for patterns among large amounts of data
.
analysing relationships between variables.
It is often not possible to see any kind of pattern in a mass of raw data, but drawing a graph – even a rough-and-ready one simply for your own purposes – can be the best way to tease out the salient points, and to identify trends or areas of concern. Once these have been identified, you may have to undertake further analysis of the figures before you can reach a decision. The easiest way to draw graphs and charts is to enter your figures into a computer spreadsheet and let it do the work for you. There are now many spreadsheet and graphics software packages that can produce a wide variety of graphs and charts. This has made the production of high-quality material much easier than it used to be and has thereby transformed the exchange of graphical information.
Bar charts In its simplest form a bar chart consists of a number of separate bars whose heights correspond to the sizes of each of the groups being illustrated. An example is shown in Figure 1. 12000 Number of notifications
10000 8000 6000 4000 2000 0
1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997
Figure 1 Notifications of food poisoning in Scotland, 1982–96 (Source: Scottish Executive website, 1999)
Activity What information does Figure 1 give you?
The numbers of notifications of food poisoning were fairly steady from 1982 to 1994, but rose rapidly from 1995. What you cannot tell from this graph is whether an increasing number of people are getting food poisoning or whether more people are contacting their CROWN COPYRIGHT ª 2004
13
MANAGING INFORMATION
doctors; increased publicity could be a contributory factor to the large increases in the last three years. The scale on the vertical axis allows you to estimate the number of cases in any given year to the nearest thousand, but you wouldn’t be able to ascertain the exact number of reports from this graph. The purpose of the graph is simply to give an overall impression of the incidence of food poisoning. Component, or stacked, bar charts A more complicated type of bar chart is the component bar chart or stacked bar chart, which allows an extra dimension of the data to be shown. The sizes of the various components that make up a bar are illustrated using different colours or types of shading and the components are always stacked in the same order. The components of the bars that represent the same item are shaded or coloured in the same way so that they can be easily compared. Have a look at the data in Table 1. A good way to examine any patterns that emerge from the data would be to draw a stacked bar chart. One thing to keep in mind is that there is usually considerable flexibility about the way graphs and charts are presented: it’s very much a creative process. By drawing some graphs for yourself, you will get a feel for some of the choices involved, and this will make you more aware of how people can, for instance, choose their scales to present their figures in the most favourable light. Table 1 Maternities with multiple births (Source: Office of Population, Censuses and Surveys, Birth Statistics 1998) Age of mother
Maternities with multiple births 1978
1988
1998
5,930
7,622
9,080
327
337
303
20–24
1,494
1,689
1,078
25–29
2,231
2,714
2,457
30–34
1,393
1,966
3,332
485
916
1,910
All ages Under 20
35 and over
Let’s consider how we might present a component bar chart using the data in Table 1. It is easier to draw a chart on graph paper than on ordinary paper because the graph paper has a grid. The first thing to do is to decide how you want your graph to look. With a component bar chart you can choose which element of the table to use as ‘classes’ – i.e. the bars – and which as the ‘components’ of the bars. In this case, for instance, you could use either the age ranges as the classes and the years as the components within each bar or vice versa. This is where creativity comes in, but it should also be tempered with an awareness of what message you want to get across. If you use the ages as the classes, your chart will show how the total number of multiple births varies across women of different ages, with a breakdown within each bar of how many of these occurred in each of the three years. If the years are used as
14
CROWN COPYRIGHT ª 2004
GRAPHS AND CHARTS
the classes, you will have a chart showing the total number of multiple births in each year, with a breakdown of the ages of the mothers who gave birth within each of the three years. For this exercise, we’ll choose the latter arrangement. The next stage – which is often the hardest part – is to choose suitable scales for the axes of your graph. The aim is to make the graph as large and clear as possible within the available space. (It’s preferable to work in pencil until you are absolutely sure that you’ve got everything right.) Fortunately, the horizontal axis does not pose much of a problem in this case as we have only three classes of data – the years – so an appropriate scale might be to make the bars 2 cm wide with 1 cm gaps between the bars. The bars need to be labelled at their centres with the class labels, in this case the years. Now let’s consider the vertical axis. With a component bar chart, the heights of the bars represent the total number of items in each class so the scale chosen needs to take account of this. Table 1 already shows the class totals, so you do not have to calculate them. The largest total is 9,080. A suitable scale would be 1 cm to 1,000 births. To make the graph easier to read, you could label the vertical axis ‘Number of births (000s)’ so that the numbers against the tick marks on the axis would be 1, 2, 3 and so on; a tick mark is the small dash made against the axis to divide up the scale. The completed axes would look like Figure 2. ,+ 5
L7.b&4 1' b*46)5 #+++5$
4 3 2 1 0 / . , +
Figure 2
,534
,544 X&a4
,554
Axes for a bar chart
Now you need to draw the bars. It is best to draw the full bar first and then to divide it into the components. With this scale it will not be possible to draw the bars to a greater accuracy than about the nearest 100 (1 mm). After the bars have been drawn, the next stage is CROWN COPYRIGHT ª 2004
15
MANAGING INFORMATION
to divide each bar; the components should always be stacked in the same order in each bar. The easiest way to work out the size of the components is to put your ruler against the scale on the vertical axis and to read off the measurement required for a strip of this size. For the first component of the first bar, the strip height needs to represent 327 women. By finding the value 327 (or 300) on the scale, you can then read off the required length of the strip from the scale on the ruler. In this case it would need to be about 3 mm long.
Activity Draw the bars and components on the labelled axes in Figure 2.
Your component bar chart is nearly complete. All you need to do now is to add a title, a note of the source of the data, and a legend or key to explain the meaning of the different components. The title could be something like ‘Maternities with multiple births: ages of mothers’ – this is written above or below the chart. Table 1 gives the source of the data, which you should write at the bottom of the chart so that anyone can refer back to the original source if they require the precise figures, which cannot be determined from the chart. I&< T0%&4 .+
