MAD of 20, 25, 30, 45 Step by Step | Mean absolute deviation

Step by step

The question

Question: find the mean absolute deviation, the MAD, of 20, 25, 30, 45.

20, 25, 30, 45

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 120.

There are 4 numbers.

120 divided by 4 is 30.

= mean = 20 + 25 + 30 + 454 = 1204 = 30

2 Distance from the mean

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

20 is 10 away from 30: 30 minus 20.

25 is 5 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 30.

30 divided by 4 is 7.5.

= MAD = 10 + 5 + 0 + 154 = 304 = 7.5

So on average, the numbers are 7.5 away from the mean.

4 Check

Let's check: the distances below the mean add up to 15.

Above the mean: 15.

The same, because the mean is the balance point.

So the distances are right!

below: 10 + 5 = 15, above: 15 = 15

Let's look back.

First: find the mean.

Then: distance from the mean.

Then: mean of the distances.

Last: check.

Answer