3.7 Extract meaningful information from data  (Page 4/5)

3 What are you asking? If you go from house to house asking people whether they have brushed their teeth that morning, you’ll no doubt find that most people do! By now most people know that it is socially desirable to use toothbrush and toothpaste, so they wouldn’t want you to think they are ignorant – and they’ll say yes, they did.

Statisticians often encounter people who lie, or who are economical with the truth. Of course, people don’t actually have to lie to make the information worthless. If you send a letter to all the people you can reach who graduated from your school 10 years ago, asking them to let you know what their current salary is, you might get back only a quarter as many answers as you asked for. But, if you work out the average of the ones who replied, wouldn’t that be good enough? Let’s have a look. The school did not have everybody’s current address, so you could not trace every­body. Is the school more likely to have the addresses of the ones who became well–known with a steady job and a constant home, or the others who floated around doing odd jobs? And the people who threw away your letter – maybe they had no­thing to brag about; the people who replied were probably proud to have others know what they earn. Maybe some even lied! It turns out that the average ob­tained under these circumstances could be totally unreliable.

4 Statisticians often experience trouble with central values.

As you know, the three central values are median, mode and mean. Say you are looking for a job, and you investigate the salaries of two possible employers. Below is a table showing the actual salaries for ten employees each in the two companies. You are told that the average salary is R14 000. Does that mean that it doesn’t matter which

you work for? No, because you don’t know what they mean by “average” – is it the mean, mode or median? As it turns out, R14 000 is the mean, but the medians are R14 000 and R5 500 respectively. Do you now know what to do? Remember that the median says that half of the people fall below that figure and half above.

The lesson is to make sure that you don’t make a judgement on one average only, especially if you don’t know which average is meant.

5 Graphs can easily fool.

Here are three graphs – let’s look at the first one.

This graph shows how a certain company’s exports increased from about R16 million to nearly R19 million in a year’s time – the months are shown on the x-axis and the amount in millions on the y-axis

The graph tells no lies – the y-axis starts at 0, and the line shows that there has been a small steady increase in the value of exports.

It is easy to read and understand.

But the Board of Directors of the company are not satisfied. They would like people to invest money in the company. To encourage them, the directors decide to get rid of all that unsightly white below and above the line by changing what the y-axis shows.