What Is Typical?

Weekly Wages
Sly Sellers received a strange request recently. The manager and the Workers' Union from the same factory each asked the agency to work out the average wage. The weekly, wages are shown in Table 5.

Table 5 - Weekly wages.

1. Copy down the table. Complete it to find the weekly wage bill.
2. How many employees are there in the factory?
3. Draw a bar chart to show the wages.

The Average?
Sly Sellers told the Union that:

'The typical weekly wage is £50. The manager earns nearly 10 times that amount. This is very unfair.'

They, told the manager that:

"The wages are quite high in the factory. The typical weekly wage (the average) is £80.'

1. How were these two typical wages worked out?

Two typical wages have been given. A third one could be the MEDIAN. To find it, put the 25 wages in order. The middle one is the median.

2. Copy and complete:
   For the wages in this small factory the arithmetic mean is £_____ the median is £_____ and the mode is £_____
3. Find the range of wages by taking away the lowest wage from the highest wage.
4. Use b and c to make a fair statement about wages in this factory.
5. Which typical wage is most useful here?

What Is Average and Is It Enough?
'Average' often just means typical.

Here are four statements which use the word 'average'. In each case the statement would be misleading. The comments in brackets are hints.

1. Come to Oklahoma for a holiday. Its average temperature is 62^oF, the same as California. (Hint: The range in Oklahoma is from 17^oF to 113^oF.)
2. The average family has 1.8 children, so we should build three-bedroomed houses. (Hint: What happens to big families?)
3. The average adult shoe size is 8, so we should make all our shoes that size.
4. The average price of houses doubled in five years. Start saving with a building society today.
   
   (Hint: Is the first house twice as big as the other? Look at lengths and areas. Is your house 'average'?)

1. Write down what is wrong with each of the four statements. (It may help to discuss the statements with a friend).
2. Copy the following:
   Statistical Point 1
   When something is called 'average', it should be explained. Is it the arithmetic mean, the median or the mode?
   Statistical Point 2
   It is important to give some idea of the variation round the average used, for instance, the range.

Look at your collection of real advertisements.

3. Do any of them forget statistical points 1 or 2?

*More Faults
Here are some more suspect statements that Fact Ferrets discovered.

1. Only half as many road accidents happen in the dark as happen in daylight, so it is safer to drive at night.
2. Most people who clean their teeth need to have fillings, so cleaning teeth is a waste of time.
3. 90% of those injured in road accidents in Australia wore seat belts. It is safer not to wear seat belts.

1. Write down what is wrong with each of these statements.

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