What is... | June 2, 2015

# What is a median?

Many professional footballers probably earn less than you think. The term “median” explains why – and is also relevant to many other situations in life.

Three types of average
There are three types of statistical average – the mean, median and mode.
The mean is perhaps most commonly used and often called “the average”. For a set of data (say footballers’ wages) it is the total of the numbers divided by how many numbers there are.
The median is the middle value – calculated by putting all the numbers in order then finding the mid-point.
The mode is the value that appears most.

Footballers’ average wages seem so high
Soccernomics author Simon Kuper wrote for eZonomics in 2012 about the wages of Italy’s Serie A team.
He told how the average player’s wage was about EUR900,000. But the median wage was much lower at about EUR500,000.
In football as in many professions, a huge slice of the rewards goes to just a few top performers and this skews up the average (as measured by the mean).
The median – the mid-point – is a way to get around this and is considered by some to be a more robust measure when there are large outliers in a data set. So if there are Wayne Rooneys or Cristiano Ronaldos earning many millions a year, a more realistic picture of team members’ fortunes might be obtained using the median.

Is my test result above average?
Another example might be results of a school exam.
The student’s result compared with the class mean will give one measure of success.
But if they want to know if they were in the top or bottom half of the class, a median is more useful.

My big day was far from average
For the ING International Survey on Weddings and Life Events 2015, the authors used the median spend for the cost of weddings in Europe to show a realistic number.
As we have seen, very high (or very low) responses can skew the result.
As the former Associate Justice of the Supreme Court of the United States Louis D. Brandeis reportedly said: “I abhor averages. I like the individual case. A man may have six meals one day and none the next, making an average of three meals per day, but that is not a good way to live.”

Finding the middle ground for you
The three different types of average – mean, median and mode – each have strengths and weakness in what they reveal.
If a mean that has been skewed upwards becomes a commonly accepted reference point – think about the cost of a wedding or holiday – it might change the way people think about their own spending.
What’s important is to remember there are different options. Consider why one measure might give a more realistic picture in certain circumstances.

eZonomics team
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