Summarising centre and spread
Most data sets exhibit variability — all values are not the same! Two aspects of the distribution of values are particularly important.
In this section, we examine how to describe centre and spread with numerical values called summary statistics. Numerical summaries of centre and spread give particularly concise and meaningful comparisons of different groups.
A pharmaceutical company is in the final stages of testing a new class of drugs that are effective at reducing high blood pressure. Some patients have however reported side effects — in particular some felt that their perception of distance had been affected.
The diagram below shows results from an experiment that was conducted to measure whether the ability to assess distance was worse for patients receiving the drugs. A 'control' group of 20 male patients were not given any drug, whereas two other groups were given drug A and drug B. Each subject was asked to position himself 3 metres from a wall and the actual distance was recorded.
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There is considerable variation in the estimates of the 3-metre distance from the patients — their estimates were up to 1 metre in error.
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A numerical measure of centre should describe this tendency to over- or under-estimate the distance.
After further development, a similar trial was conducted with two different drugs.
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There is no tendency to over- or under-estimate a 3 metre distance with these drugs — the centres of all three distributions are close to zero. However
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A numerical measure of spread should describe this tendency for greater errors with drugs C and D.