1.4 Teaching the mean

Although every learner is different, teachers often spot pupils making similar mistakes, often arising from common misconceptions.

Forgetting zero

When finding the mean, learners do not always ‘count’ 0 as a data point. For example, they might calculate the mean of 0, 0, 3 and 5 by finding the total, 8, then divide by 2 instead of 4. You might challenge this by stressing that 0 ‘counts’ as a valid measurement (and a good answer to “how many dragons are in this room?”) or by using the levelling out picture method.

Could create a little animation similar to the previous lunch bill one to show this

Video 3 Dragons per room

giving the answer 61 instead of 13.8. Can you see where the problem is?

Teachers will often recommend that students use brackets when inputting negative values into a calculator, to avoid potential input errors. That is not the problem here!

In the second calculation above, only the final value, 10, is being divided by 5, not the total of the five values before the division sign. This is because the calculator is likely programmed to use the order of operations, sometimes called BIDMAS or PEMDAS, and is therefore calculating the division before the addition.

To correct this, additional brackets around the initial sum are required, like this:

Using the fraction button to input the calculation, as in the first calculation above, naturally brackets the calculation in the numerator.

A frequent method for checking answers in mathematics is answering the question ‘does that seems sensible?’. If questioned, the response ‘it must be correct, it is what the calculator says’ is not uncommon! In this situation learners may not recognise that 61 is not a sensible answer because they see the value 72 amongst the list of numbers. The teacher could ask ‘Is that total big enough to create five 61s?’

A good check (for n values) is seeing whether n copies of the mean give the same total amount.