“With one foot in a bucket of ice water, and one foot in a bucket of boiling water, you are, on the average, comfortable.” (Bobby Bragan, 1963)
Human beings revel in their uniqueness and value their individuality, yet when it comes to data we become fixated on the ‘average’ and as the above alludes to the focus on the average means missing out on key characteristics.
In statistics the term average actually includes the three M’s:
- Mean
- what is typically meant by average
- is easy to calculate
- is influenced by outliers
- Median
- the middle number once you’ve put your data into order
- not as easy as the mean to calculate
- is not influenced by outliers
- Mode
- the number that occurs most often
- easy to determine
While it’s unlikely that you’ll ever be able to get away from the use of the average (namely the mean), you should never just calculate an average and report it or make decisions from it.
What you need to do is look at the shape of your data by looking at its histogram. Even if you do not end up using the graph, by inspecting your data graphically you’ll know what you need to include over and above the average to ensure the full story is given.
The key things to look out for in your data are:
It is the analyst’s job to convey the key characteristics, uniqueness and individuality of the data. Even if the traditional average is insisted upon (and it will be), include other key statistics and discuss why they are included and what they mean (no pun intended!).
“Then there is the man who drowned crossing a stream with an average depth of six inches.” (W.I.E. Gates)
Normal & skewed images taken from:
https://onlinecourses.science.psu.edu/stat504/node/14
Bi-modal image taken from:
http://www.nature.com/ng/journal/v39/n4/fig_tab/ng1990_F2.html
Average quotes taken from: