4.8.1 Mean
The mean is found by adding up all the values in a set of numbers and dividing by the total number of values in the set. This is what is usually meant by the word ‘average’.
For example, if a company tests a sample of the batteries it manufactures to determine the lifetime of each battery, the mean result would be appropriate as a measure of the possible lifetime any of the batteries and could be used to promote the product.
Activity 12
A sample of 15 batteries was tested. The batteries lasted, in hours:
23, 28, 25, 30, 18, 29, 23, 19, 30, 24, 25, 21, 26, 25, 23
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Calculate the mean life of a battery, correct to one decimal place (i.e. with one figure after the decimal point).
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How many hours of life will the company claim?
Discussion
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Adding up all the values gives 369. Dividing 369 by 15 gives 24.6.
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The company is likely to claim an average battery life of 25 hours (24.6 rounded up to the nearest hour).
However, the mean is not always a good representation of the data. To illustrate this, consider the annual salaries of the people employed by a small company. The salaries, in euros, are:
22 000, 22 000, 25 000, 28 000, 35 000, 65 000, 92 000
The mean salary = 289 000 ÷ 7 = 41 286 euros (approximately). Here, however, the mean is very misleading because the two highest salaries raise the mean considerably. You might like to confirm this by calculating the mean of just the five lowest salaries.