MAD of 3, 5, 6, 9, 12 Step by Step | Mean absolute deviation

Step by step

The question

Question: find the mean absolute deviation, the MAD, of 3, 5, 6, 9, 12.

3, 5, 6, 9, 12

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

MAD = the mean distance from the mean

1 Find the mean

The mean is the sum divided by how many.

The sum is 35.

There are 5 numbers.

35 divided by 5 is 7.

= mean = 3 + 5 + 6 + 9 + 125 = 355 = 7

2 Distance from the mean

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

3 is 4 away from 7: 7 minus 3.

5 is 2 away.

And so on.

Each time, bigger minus smaller.

So a distance is never negative.

= distance = bigger − smaller

Careful!

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

We would always get 0.

Careful: a distance is never negative

3 Mean of the distances

Now the mean of the distances.

They add up to 14.

14 divided by 5 is 2.8.

= MAD = 4 + 2 + 1 + 2 + 55 = 145 = 2.8

So on average, the numbers are 2.8 away from the mean.

4 Check

Let's check: the distances below the mean add up to 7.

Above the mean: 7.

The same, because the mean is the balance point.

So the distances are right!

below: 4 + 2 + 1 = 7, above: 2 + 5 = 7

Let's look back.

First: find the mean.

Then: distance from the mean.

Then: mean of the distances.

Last: check.

Answer