Averages without adding everything

Pick a middle number and only average the small differences.

The question

What is the average of 62, 65, 68, 71 and 74?

The trick

Choose a number near the middle as your base. Write down how far each value sits from it, average those small differences, and add that to the base.

Worked example

1Take 68 as the base
2Differences: −6, −3, 0, +3, +6
3Those differences add to 0, so their average is 0
4Average = 68 + 0 = 68

So: 68

Remember it like this

Stand on a middle number and measure how far everyone leans. If the leans cancel out, you're already standing on the answer.

In the exam

This is the 'assumed mean' method examiners expect for large data sets. Choose a base that appears in the list — the arithmetic stays smallest that way.

Why it works

Shifting every value down by the same amount shifts the average down by that same amount. Adding the base back at the end undoes the shift exactly.

Explain this to my childGet the words to teach it, in your language

Try it yourself

0/3 correct

1
Average of 21, 22, 23, 24, 25
Average of 21, 22, 23, 24, 25
2
Average of 48 and 52
Average of 48 and 52
3
Average of 100, 102, 104, 106
Average of 100, 102, 104, 106