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This graph still does not lie – but it fools the eye into seeing a dramatic increase in exports – starting from what looks like almost nothing.

But, by doing a bit of stretching, this same graph can be given a make-over that will appeal more to possible investors.

And here is the last version – much more impressive than number one!

See how steep the growth is – it looks as if the company is growing fiercely!

It is important to check that all the values you need to understand a graph are pre­sent. Sometimes the axes are unlabelled, which makes a graph worthless for putting across accurate information. Don’t place any faith in graphs which don’t tell the whole story – someone may be trying to pull the wool over your eyes.

Exercise.

6 Study all the graphs of all kinds you can find, and see whether all of them tell a true and reliable story. If you find any that are doubtfully accurate, bring them to class and discuss them with your teacher and the rest of the learners. A collection of poor graphs on the maths notice board will be useful to remind us not to be gullible.

7 Evaluate the following statements to see whether the speaker could be trying to mislead you. You can assume that the figures appearing in them are correct. Write down whether you need more information to be able to say what is the truth. Also try to find out what logical errors are made in the statements.

7.1 New Spediclene kills 85% of bacteria.

7.2 As nearly half of all car accidents happen over weekends, this means that people who drive during the weekend are poorer drivers than the rest.

7.3 Last year more people died in aircraft accidents than ten years ago. Therefore flying is becoming more dangerous.

7.4 A certain travel brochure states that a certain place is suitable for people who don’t like it too warm, as “the average temperature is 22 °C”.

8 Finally, here is a famous graph. It does not resemble our graphs; in fact it is much more of a map or a picture. But graphs are really only special types of pictures.

Dr John Snow was a doctor in Central London, England in the 1850’s. There was an outbreak of cholera (a very serious disease, often carried in contaminated water). He used a map of the area and on it he marked the public water pumps with crosses, and the home of every case of cholera with a dot. He noticed that the cholera cases lay closest to the Broad Street water pump. He had the handle of the pump removed and ended the epidemic during which more than 500 people had died. On the map you will see the cross for that water pump next to the word Broad.

If this section has opened your eyes to the value of graphs, you will appreciate a beautiful book written by Edward R. Tufte, called The Visual Display of Quantitative Information. You will probably have to ask a very sympathetic librarian or a university library to find out about it.

Sources:

Mathematics Teacher, December 1987

How to Lie with Statistics, Darrell Huff, Penguin Books, 1976

Getal en Ruimte, 5/6 V–A1, J H Dijkhuis et al. Educaboek (Holland), 1985

Assessment

LO 5
Data HandlingThe learner will be able to collect, summarise, display and critically analyse data in order to draw conclusions and make predictions and to interpret and determine chance variation.
We know this when the learner:
5.1 poses questions relating to human rights, social, economic, environmental and political issues in South Africa;
5.2 selects, justifies and uses appropriate methods for collecting data (alone and/or as a member of a group or team) which include questionnaires and interviews, experiments, and sources such as books, magazines and the Internet in order to answer questions and thereby draw conclusions and make predictions about the environment;
5.3 organises numerical data in different ways in order to summarise by determining:
5.3.1 measures of central tendency;
5.3.2 measures of dispersion;
5.4 draws a variety of graphs by hand/technology to display and interpret data including:
5.4.1 bar graphs and double bar graphs;

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Source:  OpenStax, Mathematics grade 9. OpenStax CNX. Sep 14, 2009 Download for free at http://cnx.org/content/col11056/1.1
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