We generally want to have a picture of what our values will look like,
and measures of central tendency basically inform about what the
'typical' value in our sample looks like. The most commonly used
measures are the mean, median, and mode.
The mean is simply what we think about when we do an average. We add
up all of our values and divide it by the number of values. This
value is very useful but its major drawback is that it can paint a
distorted picture when we have samples that don't look like a normal
distribution (bell curve). For example, in many countries a small
number of people are so wealthy that when you do an average, the mean
might actually be skewed to a larger value, making it appear that the
population is actually well off economically speaking, when in fact it
may not be. A better measure is the median, which is the value that
corresponds to the halfway point in a sample. To get the median, you
must first order your values from smallest to greatest, and then find
the value that is smack dab in the middle of them. If that value is
"in-between", such as if you have an even number, just average the two
values together. The reason why the median is better than the mean is
because even if we have a very high or low value, the middle value
will always remain the same because it is based on the number of data
points (observations) and not their values. Finally, the mode is a
measure that informs about the most common value in a sample; that is,
it is the value most highly occurring in a sample distribution. The
bell curve, for example, has just one mode.
The mean, median, and mode should be the same if the distribution is
normal. (Why?) The reason is because the middle value will be at the
mean, and all values are exactly mirrored to the left and right of it
(Best way to imagine this is to actually draw a picture).
We would like to get as complete a picture of our data as possible.
What might happen if, for example, we have a curve where we visualize
two equally sized 'peaks' to the left and right of the center? Simply
using the mean and median, here, would not give us a good idea because
a large number of values are farther away from the mean or median.
The mode, however, might tell us that there are two frequently
occurring values here. What might happen if the bulk of our data is
skewed to one side but there are a few extremely large values on the
other side? Our mean might not be as useful as the median.
Try and draw a few pictures of data distributions and compare them to
the bell curve normal, and see what might happen to the mean, median,
and mode. |
