Diagram of equation

Just about average

There are different types of average

When we talk about ‘an average’, what we’re really trying to do is get some sense of where the middle is. We can then use that as a way of comparing two groups of data. Unfortunately, there isn’t just one type of average – there are several.

To get the mean, add the data together and divide the total by how many data points there are (see equation). Beware, though – outlying data can often skew the mean to be artificially high or low.

Take the following number list: 1, 3, 6, 9, 9, 11, 14. The mean here is 7.57. However, add a much higher number to the end of the list, say 50. The mean is now 12.88. Just one particularly large outlier has almost doubled the mean, and the majority of the numbers are below the mean. Imagine how the mean wealth of biology teachers in a room might change if Bill Gates joined them.

If you place the numbers in ascending order and look for the middle value in the list, you have the median. If there are an even number of values, you take the mean of the middle pair. For the original list, this is 9. Outliers have a much smaller effect on the median than the mean, so adding 50 again does not alter the median.

The mode is the value that occurs most often in a list. For this list, the mode is 9.

About this resource

This resource was first published in ‘Number Crunching’ in June 2013.

Topics:
Immunology, Statistics and maths
Issue:
Number Crunching
Education levels:
16–19, Continuing professional development