There are three measures of central tendency: the mean, the median, and the
mode. Now we will talk about the median. The median is another name for the score
at the 50th percentile, the score at the geographic center of the data. If the
median is 10, then half of the scores are at or below 10 and, of course, half of the
scores are above 10 to calculate the median you must first put your data in
ascending order.
This is not optional, Once you have arranged your data in ascending order,
you would then count halfway through the distribution and find the middle
number. Now, if the total number in your sample is odd then the median will be a
single number that's located in the (n + 1)/2 position. Now if the total number
in your sample is even, then the median is actually between two numbers that are
located in positions (n / 2) and (n / 2) + 1. If the numbers are the same, then that is
your median. But if the numbers are different, then you would average them to
find the median. Now I know this is a little complex. It's actually easier to see if
we practice, so let's do that. In Data set C, what is the middle number?
We count in four from either side, and we find that the median is 3 because this is an
odd number of data points, the median is exactly in the middle. But now look at
Dataset D, as we count in we find that the median is actually between 12 and 13,
so we average those numbers (12 + 13) / 2. The median is 12.5. So again, when
there are an odd number of data points, the median will be a middle number. When
there are an even number of data points the media will be between two numbers
that we must then
average. The measure of central tendency that you choose to report depends upon
your data, so it's important to know when we should choose the median instead of
the mean or the mode. One advantage of the median that makes it better than the
mode is that it can only have one score. It can only be one number, and this
avoids the problem that we have with a bimodal distribution. On the other hand,
the median will not always be one of the actual scores in the data set. You recall
that calculating a median sometimes involves averaging two numbers and
getting a median that's not an actual data set value. The median can be useful
with highly skewed data, and this is because the median is minimally
susceptible to outliers. Adding an outlier, no matter how large, moves the
median toward the outlier one space at a time, so if one of the lab rats goes to
sleep in the maze, the median time can still be useful.
The median is the preferred measure when your data are measured at the ordinal
level. When your data are rank ordered the median usually provides a whole
number that is one of the actual data points of item response. The median is
not useful with nominal data. Remember that the first step to calculate the
median is to put the scores in ascending order. Nominal data cannot be rank
ordered, so it makes no sense to say that 60% of voters prefer a
Democrat or below. So think of the median like the median in a road. The median
runs right down the middle.
You should report the median when your variables are measured at the scale
level but are highly skewed or when your variables are measured at the ordinal level.