What is the "Median?"

The "median" is another type of average value. It is a summary statistic obtained by finding the middle value of a data set. Sorting the data always helps to find the median. For example; the median of 1, 3, & 4 is 3. If there happen to be an even number of data points, the median lies between the two values in the center. For example; the median of 1, 3, 4, & 5 is 3.5. But what does this number tell us about the data?

The "Median" Is the Middle Value

The "median" divides the data in half. It is the middle value. Half of the data points are above it and half the data points are below it. Therefore, it is a very useful number to know!

Unfortunately, to determine the median you need to have access to all of the data. Knowing just the total value and number of data points just isn't enough. You need to also know how the data is distributed...

Data distribution are often represented by a histogram. A histogram is a wonderful way to show your data. By looking at a histogram you can immediately see the "mode" (highest point) and can quickly estimate the "median" (it cuts the data into equal parts). You can also tell if the "mean" is above or below the "median" by looking for the extreme values.

So if we think of the data as a pet snail, the "mode" is at its shell (highest point), the "median" is the middle (divides it into two equal halves), and the "mean" is located closer to its head (extreme values). If the snail happens to be symmetrical; the "mode", "median", and "mean" all coincide. But this rarely happens with real data (or more precisely; it happens frequently in theory, but rarely in practice).