MAD of 6, 9, 12

Step by step

The question

Question: find the mean absolute deviation, the MAD, of 6, 9, 12.

The MAD says how spread out the numbers are: on average, how far each one is from the mean.

1 Find the mean

The mean is the sum divided by how many.

The sum is 27.

There are 3 numbers.

27 divided by 3 is 9.

2 Distance from the mean

We make a table: each number, and how far it is from the mean.

6 is 3 away from 9: 9 minus 6.

9 is 0 away.

And so on.

Each time, bigger minus smaller.

So a distance is never negative.

Careful!

If we used minus signs, the numbers below the mean would cancel the ones above.

We would always get 0.

3 Mean of the distances

Now the mean of the distances.

They add up to 6.

6 divided by 3 is 2.

So on average, the numbers are 2 away from the mean.

4 Check

Let's check: the distances below the mean add up to 3.

Above the mean: 3.

The same, because the mean is the balance point.

So the distances are right!

Let's look back.

First: find the mean.

Then: distance from the mean.

Then: mean of the distances.

Last: check.