Table 12.1 Graphs for presenting numerical data and when to use them

Graph	Use when you want to present data to
Histogram	show frequency of occurrence and emphasise highest and lowest categories for one variable show the distribution of categories for one variable (frequencies are normally displayed vertically and categories horizontally and the data values will need to be grouped into categories)
Line graph	show the trend for one variable over time
Multiple line graph	compare the trends for two or more variables over time
Scatter graph	show the relationship between the individual cases for two variables
Frequency polygon	show frequency of occurrence and emphasise highest and lowest categories for one variable show the distribution of categories for one variable (frequencies are normally displayed vertically and categories horizontally, and the data values will need to be grouped into categories)
Box plot	show the distribution of values for one variable and present statistics such as the median, quartiles, range and inter-quartile range
Multiple box plot	compare the distribution of values for two or more variables and present statistics such as the median, quartiles, range and inter-quartile range

Histograms are the numerical data equivalent of bar charts. They are especially useful when you want to emphasise the highest and lowest values or the distribution of values for a variable. Before drawing your histogram you will nearly always need to group your data into a series of groups along a continuous scale. This means you will need to:

(i) decide on the classes into which to group the variable’s data;

(ii) create a frequency table recording the number of times values occur in each of these classes;

(iii) draw your histogram using a bar to represent the frequency with which values occur in a class.

The main differences between the appearance of a bar chart and a /histogram are as follows:

• The horizontal axis has a continuous scale, and is represented by the bars of data being joined together.
• The area, not the height, of each bar represents the frequency. This is extremely important if you are using classes of different sizes.

Line graphs should be used when you want to present what is happening over time, the trend being represented by the line. On line graphs, the horizontal axis is used to represent time, and the vertical axis the frequency, the data values for the time periods being joined by a line.

When you want to compare trends for two or more variables over time, you just plot an additional line for each additional variable.

Scatter graphs, also called scatter plots, are used to show the relationship between two numerical variables. Where you have an independent and a dependent variable, the horizontal axis is used to represent the independent variable (the one that is the variable manipulated (altered or changed) to find out its effect on another variable) and the vertical axis to represent the dependent variable (the one that is measured in response to the manipulation of the independent variable). However, you can use scatter plots to show relationships where you do not know which variable is dependent and which is independent. Each case’s position on the graph is plotted against the two variables, normally being represented by a cross. The strength of any relationship is represented by the closeness of the crosses plotted to an imaginary straight line.

Final comments. You will no doubt have noticed that we have not included any three-dimensional graphs in this chapter. This is because we believe that they do not present data as clearly as two-dimensional graphs.

1. Complete the following sentences:
• It is necessary to group the values…

· Once you have grouped the data for your numerical variables…

· There is a wide range of graphs that…

· Histograms are especially useful when …

· Before drawing your histogram you will nearly always need …

· The main differences between the appearance of a bar chart and a /histogram are …

· Line graphsshould be used when you want…

· Scatter graphs, also called scatter plots, are used to show..

· The strength of any relationship is represented by …