It seems that it can be relatively easy to work out the mode, median
and mean. But why would anyone want to know all or any of these
values? All of these can tell us something about a set of observations.
Generally the mode tends to be reported little.
It is not a measure of centre in the same way that median and mean
can be. However, mode is the only measure of centre appropriate
for nominal data. For example, if we were looking at the most
frequently purchased food item in the Foodhall in 1999, it does
not make sense to talk about the median food or the mean food but
it does make sense to say that the most frequent (modal) food purchased
was (shall we say) mini chocolate bars.
Sometimes there might be more than one mode in a set of data –
it is possible that the most popular food item purchased was lamingtons
and mini chocolate bars.
The median is at the middle of an ordered (ranked) data set and
is a useful measure for ordinal variables.
Strictly speaking, the mean only makes sense for interval and ratio
scales of measurement. However, there is a tendency to calculate
means for ordinal variables as well. The calculation of a mean for
ordinal scales of measure assumes that the interval between the
rankings is the same between each ranking [16].
But, can we be sure that my idea of the interval between 'agree'
and 'strongly agree', for example, is the same as yours? An example
of this type of scale is rating scales. These scales are divided
into intervals and usually numbered similar to the method used in
the example below.
However, although the scale implies that the intervals
are equal, they are not intrinsically equal.
Usage of mean and median compared
Sometimes the mean is thought of as an economic measure
and the median as a social measure. For example, the mean
income of a group of people might be of more interest to retailers
and the tax office, but the median income might be of more interest
to welfare organisations. In the calculation of the mean, these
groups are interested in the total amount that is available (in
this case it is money) but welfare groups are interested in the
number of units that this amount is distributed amongst.
In real estate usage, the mean would be used to describe the average
value of a portfolio of houses being offered for sale by a real
estate agent. However, someone wanting to buy a home from that real
estate agent would use the median or middle house value. This is
because the median does not alter when there are extreme values
(outliers) in a data set.
To illustrate:
Set A: 30 40 50 60 70 has mean = 50 and median = 50
Set B; 30 40 50 60 700 has mean = 176 and median = 50
The value 700 is an outlier because it is a long way from the next
nearest data value, 60. On the other hand, 70 is not a long way
from 60.
SCENARIO
Last year, a fast food outlet in a beachside city paid
3 kitchen hands $16000 per year, 2 supervisors $22000
and the owner $85000.
The mean salary at this business was $30000 and the
median was $19000 (the mean of the two centre observations
in an ordered list). The mode was $16000.
