There are three measures of central tendency: the mean, the median, and the
mode. Let's begin with the mode. The mode is the most frequently occurring score.
The mode would then be the score with the highest frequency. If there is one
most frequently occurring score, one mode, we call that a unimodal distribution.
A unimodal distribution has only one major peak. Now in other cases, there may
be two modes. A bimodal distribution has two major peaks. The mode is most
commonly used with nominal level data when there's one category that is likely
to be the most popular. When the distribution is bimodal, typically it's
for one of two reasons. The first: there really maybe two modes. For example, if
you plot the number of fish caught by fishermen, we see a peak in the morning,
at dawn, and another peak in the evening, at dusk. In the middle of the day, when
the sun is at its height, fewer fish are caught. This would be a true bimodal
distribution. The second time you see a bimodal distribution is when there are
actually two distributions overlapping each other. If we compare average IQ
scores from a state university and a community college and we find a bimodal
distribution, we might want to split our data by school to see if we are really
dealing with two distinct distributions of scores. Because they are two different
groups, you should separate them before analyzing the data set. The mode is most
commonly used with nominal data. For example, if we took a poll of a class
asking what flavor of ice cream they prefer, one flavor would be the most
popular. That most frequently chosen flavor would be the mode. To calculate
the mode, it is very useful although not absolutely necessary
to arrange the scores in ascending order from lowest to highest to see which
score occurs most frequently. So look at the values and data set A and see if you
can figure out the mode. There are more fours than any other number, so the mode
is four. It is the most frequently occurring score. Now look at data set B.
What is the mode? You'll see there are actually two most frequently occurring
scores: five and nine. So this is a bimodal distribution with modes at five
and nine.
Incidentally, when you get the mode in SPSS and the distribution is bimodal,
SPSS will tell you the smallest mode. In this case it would be five, and then give
you a warning that multiple modes exist. The measure of central tendency that you
choose to report depends upon your data. So it is important to know when you
should choose the mode instead of the mean or the median. The biggest advantage
of the mode is that it is not susceptible to outliers at all.
Any outlier no matter how large has absolutely no effect on the mode.
Remember that an outlier is a score that is significantly higher or lower than
most of the other scores. The advantage to the mode is also its disadvantage.
The mode ignores most of the data by not considering scores other than the most
frequent. So for example if the scores were 7, 7, 20, 21, 22, 23, 24, the mode is seven.
But that mode of seven is misleading because most of the scores are not
around 7 so 7 is non-representative. The median of 21 would be a more
representative score. Another disadvantage to the mode is that it's
not terribly useful when the most common score for behavior being measured is 0.
So how many cigars have you smoked in the last month? There may be two people
in class who have smoked a cigar, but our mode of 0 doesn't tell us anything about
those people of interest. You should report the mode
when there is one particular score that dominates the distribution. This occurs
with nominal level data such as when we want to know the most popular category
or the most commonly selected product. Report the mode when the distribution is
bimodal--when the mean or the median would be non-representative. The mode is
the central tendency measure of choice when the variables are measured at the
nominal level. Nominal level variables will be analyzed using a nonparametric
test. Finally, the mode can be a quick and easy way to get a sense of
your ordinal or scale variables when you are first approaching a dataset.