The Mode
The mode is the most commonly occurring score. By definition, then, it is a score that ac-
tually occurred, whereas the mean and sometimes the median may be values that never ap-
pear in the data. The mode also has the obvious advantage of representing the largest
number of people. Someone who is running a small store would do well to concentrate on
the mode. If 80% of your customers want the giant economy family size detergent and 20%
want the teeny-weeny, single-person size, it wouldn’t seem particularly wise to aim for
some other measure of location and stock only the regular size.
Related to these two advantages is that, by definition, the probability that an observa-
tion drawn at random ( ) will be equal to the mode is greater than the probability that it
will be equal to any other specific score. Finally, the mode has the advantage of being ap-
plicable to nominal data, which, if you think about it, is not true of the median or the
mean.
The mode has its disadvantages, however. We have already seen that the mode depends
on how we group our data. Another disadvantage is that it may not be particularly representa-
tive of the entire collection of numbers. This disadvantage is illustrated in the electronic game
data (see Figure 2.3), in which the modal interval equals 0–9, which probably reflects the fact
that a large number of people do not play video games (difficult as that may be to believe).
Using that interval as the mode would be to ignore all those people who do play.
The Median
The major advantage of the median, which it shares with the mode, is that it is unaffected
by extreme scores. The medians of both (5, 8, 9, 15, 16) and (0, 8, 9, 15, 206) are 9. Many
experimenters find this characteristic to be useful in studies in which extreme scores occa-
sionally occur but have no particular significance. For example, the average trained rat can
run down a short runway in approximately 1 to 2 seconds. Every once in a while this same
rat will inexplicably stop halfway down, scratch himself, poke his nose at the photocells,
and lie down to sleep. In that instance it is of no practical significance whether he takes 30
seconds or 10 minutes to get to the other end of the runway. It may even depend on when
the experimenter gives up and pokes him with a pencil. If we ran a rat through three trials
on a given day and his times were (1.2, 1.3, and 20 seconds), that would have the same
meaning to us—in terms of what it tells us about the rat’s knowledge of the task—as if his
times were (1.2, 1.3, and 136.4 seconds). In both cases the median would be 1.3. Obvi-
ously, however, his daily mean would be quite different in the two cases (7.5 versus 46.3
seconds). This problem frequently induces experimenters to work with the median rather
than the mean time per day.
The median has another point in its favor, when contrasted with the mean, which those
writers who get excited over scales of measurement like to point out. The calculation of the
median does not require any assumptions about the interval properties of the scale. With
the numbers (5, 8, and 11), the object represented by the number 8 is in the middle, no mat-
ter how close or distant it is from objects represented by 5 and 11. When we say that the
mean is 8, however, we, or our readers, may be making the implicit assumption that the un-
derlying distance between objects 5 and 8 is the same as the underlying distance between
objects 8 and 11. Whether or not this assumption is reasonable is up to the experimenter to
determine. I prefer to work on the principle that if it is an absurdly unreasonable assump-
tion, the experimenter will realize that and take appropriate steps. If it is not absurdly un-
reasonable, then its practical effect on the results most likely will be negligible. (This
problem of scales of measurement was discussed in more detail earlier.)
A major disadvantage of the median is that it does not enter readily into equations and
is thus more difficult to work with than the mean. It is also not as stable from sample to
sample as the mean, as we will see shortly.Xi34 Chapter 2 Describing and Exploring Data