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

Year 2007 2008 2009 2010 2011
Rainfall, in inches (to 1 d.p.) 5.8 5.2 4.6 9.3 4.5
Reference Enloe, Jesse. “Vermont Precipitation October 1895-2011.” National Oceanic and Atmospheric Administration Climatic Data Center, National Environmental Satellite, Data, and Information Service (NESDIS), U.S. Department of Commerce. Available online at http://www.ncdc.noaa.gov/temp-and-precip/time-series/index.php (accessed December 22, 2011).

Solution symbolActivity: How Wet is it in Vermont?

Find the mean rainfall in Vermont in October for these five years.

Solution symbol

Answer

The sum of the five data values is: sum with, 5 , summands 5.8 plus 5.2 plus 4.6 plus 9.3 plus 4.5 equals 29.4.

The mean rainfall is 29.4 in divided by five equals 5.88 in.

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.

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Calculating the Median Rainfall in Vermont

To find the median rainfall, first arrange the data values in order:

4.5 4.6 5.2 5.8 9.3

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!

11.1.2 Using a Calculator to Find the Mean

11.1.4 More Means and Medians