Question

When might the median be the better measurement of average for a data set?

Answer 1

Good Question!

Medians prove to be the most useful when the data is strongly skewed.

For example:

Take a look at the image below, created by Statistics How To

You can see that the median looks like it best represents the data. Not too much on the peak, or the tail.

-------------------------------------------------------------------------------------------------------

Symmetrical Data example

$(1, 2, 3, 4, 5, 6, 7, 8, 9, 10)$

The average of this data set is 5.5.

The median is also 5.5

There is no mode; no numbers repeat.

Because this data is symmetrical, the mean may be the best measure of center. It can depend. One could also say that both the mean and median are equally useful.

-----------------------------------------------------------------------------------------------------

Outliers also have an effect.

For example, when there is very influential outlier, the mean may become distorted.

For example:

$(1, 2, 3, 4, 5, 6, 7, 8, 9, 207)$

207 is clearly an outlier.

The average of this data set is 25.2.

But that number is just not a logical representation of the data!

We automatically know there is no mode.

So even though 5.5 (the median) might not be perfect, it is much better than 25.5.

Therefore, the median is the best measure of center in this case.

It all depends, remember!

-------------------------------------------------------------------------------------------------------

Please let me know if this helped or if you have any questions!