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?