How to teach mean, median and mode

Grade 4 to Grade 6

An average is a single number that stands in for a whole set of data. There are three kinds. The mean is the total shared out equally (add them all, then divide by how many). The median is the middle value once the data is in order. The mode is the value that appears most often. The word 'average' on its own usually means the mean.

How to teach it

1. Teach the mean as fair sharing: pool everything, then split it equally. Add the values and divide by how many there are.
2. Teach the median by putting the numbers in order first, then finding the middle one; with an even set, take the mean of the middle two.
3. Teach the mode as the most frequent value, noting there can be more than one, or none at all.
4. Use the same small data set for all three so students see they can give different numbers.
5. Discuss which average suits the data: the mean is pulled by an extreme value, the median is not.

Worked example

Data: 3, 7, 7, 2, 6

   mean:   (3 + 7 + 7 + 2 + 6) / 5 = 25 / 5 = 5
   median: order 2, 3, 6, 7, 7 -> middle is 6
   mode:   7 appears most -> 7

Common mistakes

• Forgetting to put the numbers in order before finding the median.
• Dividing by the wrong count when finding the mean.
• Confusing the three, giving the mode when the mean is asked for.
• Letting one very large or small value distort the mean without noticing.