Mean, median or mode: which average tells the truth?

An average is one number that stands for a whole set of data. It is handy: instead of reading out 28 sleep times, you can say 'we usually sleep about nine hours'. But there are three common kinds of average, and they don't always agree.

The three averages

The range tells you how spread out the data is: the largest value minus the smallest. Two classes can have the same median sleep time but very different ranges.

When they disagree

Imagine five students' weekly pocket money: $5, $5, $10, $10 and $120. They add up to $150, so the mean is $150 ÷ 5 = $30. But four of the five students get $10 or less, so $30 is not a fair picture. The median, $10, tells the story better. The $120 is an outlier: a value far away from the rest. Outliers drag the mean towards them but hardly move the median.

Is an outlier a mistake? Sometimes. A sleep time of 90 hours is a typing error. But some outliers are real and rare: a day with 150 mm of rain in a storm, or one student who lives a long way from school. You don't delete a real outlier just because it is inconvenient. You keep it, point it out and explain it.

Choosing the right one

Use the median when there are outliers or the data is lopsided (skewed). Use the mean when the data is fairly even with no big outliers. Use the mode for categories, or to show the most common value.

Whichever you choose, show the graph too. One number can hide a lot; a graph shows the shape, the middle and the spread all at once.