11.1.3 Finding the Median of a Data Set
One of the advantages of using the mean as an average value is that it takes account of all the values in the data set. However, this also means that if one of the values is much higher or lower than the other values in the data set, it can greatly affect the mean.
Suppose you are planning a visit to Vermont, USA in October, and you want an idea of how much rainfall there will be. You consult records from the National Climate Data Center and find the following:
Precipitation (rainfall) in Vermont in October for 2007–2011
|Rainfall, in inches (to 1 d.p.)||5.8||5.2||4.6||9.3||4.5|
Activity: How Wet is it in Vermont?
Find the mean rainfall in Vermont in October for these five years.
The sum of the five data values is: .
The mean rainfall is .
Over these five years the mean rainfall was 5.9 inches (to 1 decimal place).
Now look at the five data values again. Does 5.9 inches give you a good idea of how much rainfall there has been? If the data values are plotted on a line, they look like this.
You can see that in four out of the five years, rainfall was below the mean, while it was above the mean in only one year. In that year, the rainfall was particularly high and this has pulled the mean up. So the mean is perhaps not a particularly good choice for a typical value in this case.
Let's take a look at an example in this pencast (click on “View document”).
Calculating the Median Rainfall in Vermont
To find the median rainfall, first arrange the data values in order:
There are five data values—an odd number—so choose the middle value, 5.2.
Therefore the median rainfall is 5.2 inches.
Looking at the data displayed on the numberline and where the median value falls it appears the median may be a better choice for an average or typical value in this case.
Now try out the following activity yourself!