The mean is a 'measure of central tendency'. It is a single value that attempts to tell you the position of the 'center' of the data set. There are several other measures of central tendency that try to capture the same idea, the two most important are the 'median' and the 'mode'.
Consider the following example, valuations gathered from recent house sales in a particular neighborhood were as follows:
$185,000
$190,000
$145,000
$220,000
$1,060,000
$200,000
$170,000
The mean of these values is $310,000.
A statistic only serves a purpose if it helps to inform a decision. You might want to know the average valuation because you are considering moving to the neighborhood. You would find the mean value misleading, the typical valuation is around $200,000 but one very expensive property inflates the mean.
You might find the 'median' value more useful. The median is the central value in the ordered data set, there are as many values above the median as below. To calculate it, sort the values into order and take the central value:
$145,000
$170,000
$185,000
$190,000
$200,000
$220,000
$1,060,000
The ages of people presenting with a particular medical condition were:
20
24
22
65
20
20
In this case there is an even number of values, and so no middle value. The median is the mean of the two middle values, after the data are sorted into order of magnitude:
20
20
20
22
24
65
The median is 21.
Again, the mean age of 28.5 is not meaningful. Most people presenting are young, but there is one 65 year old.
The American Medical Association (AMA) and the American Bar Association (ABA) had a dispute about the rising cost of malpractice insurance for doctors. The doctors used the 'mean' to show a sharp rise in cost over the period concerned. The lawyers used the 'median' to show there had been no increase in cost.
The 'Average Net Worth' or the 'Median Net Worth' is often used to measure the prosperity of the community.
Which do you think is the better measure, and do you think there would be much difference?
