Mean, median and outliers — Data, 14–17 years
Different centres tell different stories about the same list of numbers. Data, 14–17 years.
The idea
A measure of centre gives one number that represents a whole set. The mean shares the total equally among the values; the median is the middle value after sorting. An outlier is a value far from the others, and it can pull the mean towards it while leaving the median almost unchanged.
Why we need it
A long list is hard to compare or discuss, so we compress it into a useful centre. The problem is that “average” can hide important differences: two teams may have the same mean score but very different typical scores. Choosing mean or median depends on the question and on whether unusual values are part of the story or errors.
Worked example
Consider the waiting times 4, 5, 5, 6 and 20 minutes. The mean is (4 + 5 + 5 + 6 + 20) ÷ 5 = 40 ÷ 5 = 8 minutes. The sorted list has 5 as its middle value, so the median is 5 minutes. Because 20 is unusually high, the median better describes a typical wait, while the mean honestly includes that long delay.
The common trap
People often choose the mean automatically because it is the number called “average” in everyday speech. That is reasonable: the mean uses every value and is easy to calculate. But one extreme value can make it unrepresentative. Always inspect the data first, then say which centre you chose and why.
Where it is used
Median house prices help describe a housing market without one luxury property dominating the result. Mean reaction time can be useful when every measurement matters, such as repeated laboratory trials. Sports tables, travel reports and salaries use centres too, but a responsible report states which measure was used rather than treating every “average” as the same.
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