Measures
of Central Tendency
There
are three measures of central tendency and each one
plays a different role in determining where the
center of the distribution or the average score
lies. First,
the mean is often referred to as the statistical
average. To
determine the mean of a distribution, all of the
scores are added together and the sum is then
divided by the number of scores. The mean is the preferred measure of central tendency because
it is used more frequently in advanced statistical
procedures, however, it is also the most susceptible
to extreme scores.
For example, if the scores ‘8’ ‘9’
and ‘10’ were added together and divided by
‘3’, the mean would equal ‘9’.
If the 10 was changed to 100, making it an
extreme score, the mean would change drastically.
The new mean of ‘8’ ‘9’ and ‘100’
would be ’39.’
The
median is another method for determining central
tendency and is the preferred method for highly
skewed distributions.
The media is simply the middle most occurring
score. For
an even number of scores there will be two middle
numbers and these are simply added together and
divided by two in order to determine the median.
Using the same distribution as above, the
scores ‘8’ ‘9’ and ‘10’ would have a
median of 9. By
changing the ‘10’ to a score of ‘100’
you’ll notice that the median of this new
positively skewed distribution does not change.
The median remains equal to ‘9.’
Finally,
the mode is the least used measure of central
tendency. The
mode is simply the most frequently occurring score.
For distributions that have several peaks,
the mode may be the preferred measure.
There is no limit to the number of modes in a
distribution. If
two scores tie as the most frequently occurring
score, the distribution would be considered bimodal. Three would be trimodal, and all distributions with two or
more modes would be considered multimodal
distributions.
Figure
8.5: Measures of Central Tendency
Interestingly,
in a perfectly normal distribution, the mean,
median, and mode are exactly the same.
As the skew of the distribution increases,
the mean and median begin to get pulled toward the
extreme scores.
The mean gets pulled the most which is why it
becomes less valid the more skewed the distribution.
The median gets pulled a little and the mode
typically remains the same.
You can often tell how skewed a distribution
is by the distance between these three measures of
central tendency.
