11.6.1 Reading a Graph with Caution!

Solution symbolActivity: Cutting the Cost of Heating

The graph below shows the monthly heating bills of a house, before and after attic insulation was installed.

Use this graph to answer the following questions.

(a) Which of the principles in the Drawing Graphs and Charts box have not been followed?

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Answer

(a) No source is stated, so you have no idea how the data were collected or how reliable the information may be. Was just one house used in the survey, or were many houses used? The axes are labeled but the scales are not marked.

Suppose the scale on the vertical axis was from $120 to $121. Then the apparent drop in the bill after insulation would be negligible. However, if the scale went from $0 to $130, the drop might be of more interest.

No scale is marked on the horizontal axis, either. In fact, the data was collected from November to September, so the horizontal scale should have indicated this.

(b) What does the graph appear to show?

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Answer

(b) The graph appears to show a large drop in the heating bills after insulation was installed. However, without the scale on the vertical axis, it is impossible to say what kind of drop this is.

From the data, the drop in the monthly heating cost occurred in the May bill just as the weather was warming up for the summer. The reduced bills could simply be due to less heating being used in the summer.

Overall, no conclusions can be made from this graph about the effectiveness of the insulation.

The last activity illustrated an important point: when you are comparing two sets of data, you need to compare like with like. You would expect the bills for the summer to be less than those in the winter anyway, regardless of the presence or absence of attic insulation. It would be more appropriate to consider the amount of energy used for heating over two periods with similar weather.

Alternatively, you could compare two similar groups of houses, one group with the insulation and the other without, over the same period of time. So although graphs and charts are very useful, it is important to read them critically, checking that all the information you need to interpret them is provided.

Another important point to note when interpreting a graph is that if the graph appears to show an association between two quantities, it does not prove that one has caused the other. For example, suppose the number of students in a town registering in a math course rose from year to year and the number of burglaries in the town also rose.

Does this mean that the math students have committed the burglaries? No, of course not! Both rises may be linked to some other factor such as the number of people who have recently moved into the town.

However in other situations, it may be much more tempting to suggest that one thing has caused another—for example, if the number of cancer cases are higher around nuclear power plants than elsewhere. In order to establish cause and effect, very large statistical surveys and analyses have to be carried out.

Media Icon This short video clip [Tip: hold Ctrl and click a link to open it in a new tab. (Hide tip)] describes how the link between smoking and lung cancer was investigated.

11.6 Reading and Drawing Graphs and Charts—A Summary

11.7 Data Visualization