Selecting the Appropriate Statistical Diagram

Begin with the data and the purpose

A statistical diagram is useful only if its structure matches the data. Before choosing one, ask two questions:

1. What kind of data are on the horizontal axis? Are they categories, ungrouped discrete numbers or times?
2. What should the reader notice? Is the aim to compare frequencies, show proportions of a whole or reveal change over time?

For example, “bus”, “car” and “walk” are categories, whereas numbers of goals such as $0,1,2,3$ are discrete numerical values. Temperature is continuous because values between two recorded temperatures are possible. This classification narrows the choice of diagram.

Categories: bar chart, pictogram or pie chart

A bar chart is usually the clearest choice when the aim is to compare category frequencies. Each category has its own bar, so the bars are separated by gaps. Their heights can be read against a frequency scale, making differences reasonably easy to compare.

A pictogram also represents categorical frequencies, but it uses repeated symbols instead of bars. It can make a small, simple data set visually accessible. A key is essential: if one symbol represents four pupils, half a symbol represents two pupils. Pictograms become awkward when the key produces complicated fractions of symbols, so a bar chart is often better for precise or numerous values.

Choose a pie chart when the important idea is how a whole is divided among categories. The complete circle represents the total and each sector represents a category's proportion of it. This makes a pie chart suitable for questions such as how a budget is divided. It is less effective for reading exact frequencies or comparing similarly sized sectors. A pie chart also needs a meaningful total: unrelated values that are not parts of one whole should not be forced into a circle.

The same categorical data might therefore be shown correctly in more than one way. The best choice depends on the purpose: use a bar chart for clear frequency comparisons, a pie chart to emphasise proportions, or a pictogram for a small and simple display.

Ungrouped discrete numbers: a vertical line chart

When the possible values are separate numerical values, a vertical line chart is appropriate. For the number of siblings, for instance, the horizontal axis might contain $0,1,2,3,\ldots$, and a vertical line above each value shows its frequency.

The separate lines communicate that the values are discrete: values such as $1.6$ siblings are not possible. Although a vertical line chart resembles a bar chart, the distinction matters. A bar chart's horizontal positions name categories; a vertical line chart's horizontal positions lie on a numerical scale.

This chart is specified for ungrouped discrete numerical data. If numerical observations have already been combined into intervals, a different kind of diagram may be needed. In particular, grouped continuous data are represented using histograms, which are studied separately.

Data in time order: a time-series line graph

If observations were recorded over time, choose a time-series line graph. Time goes on the horizontal axis and the measured quantity goes on the vertical axis. Joining successive plotted points helps the eye follow changes and identify an overall trend or a repeating pattern.

The reason for joining the points is the time order, not simply that the data are numerical. Suppose a shop records its takings each month: a line graph shows how the takings develop from one month to the next. Rearranging the months would destroy that meaning.

Treat a joining line carefully when measurements were taken only at particular times. If sales were recorded quarterly, a point halfway along a line is not automatically an observed sales figure. The line displays the pattern between recorded points; it does not create new evidence.

Tables can be the clearest display

A frequency table lists each category or value alongside its frequency. It is often the best starting point because it preserves exact values and can then be used to construct a chart. If the main purpose is simply to look up exact frequencies, a compact table may be clearer than a picture. A graph or chart becomes more useful when comparisons, proportions or trends need to stand out.

Make and justify a final choice

A good justification links the diagram directly to both the data and the purpose:

• “A bar chart is suitable because the data are categorical and the frequencies need comparing.”
• “A pie chart is suitable because the categories form one whole and the proportions are important.”
• “A vertical line chart is suitable because the horizontal values are ungrouped discrete numbers.”
• “A line graph is suitable because the observations are in time order and the change over time needs to be shown.”

More than one diagram can sometimes be valid, but one may communicate the required feature more effectively. Selection is therefore not just naming a chart associated with a data type; it is deciding what representation will make the intended comparison honest and clear.