MAD of 2.5, 3.5, 4, 6 Step by Step | Mean absolute deviation

Step by step

The question

Question: find the mean absolute deviation, the MAD, of 2.5, 3.5, 4, 6.

2.5, 3.5, 4, 6

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 16.

There are 4 numbers.

16 divided by 4 is 4.

= mean = 2.5 + 3.5 + 4 + 64 = 164 = 4

2 Distance from the mean

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

2.5 is 1.5 away from 4: 4 minus 2.5.

1.5

3.5 is 0.5 away.

0.5

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 4.

4 divided by 4 is 1.

= MAD = 1.5 + 0.5 + 0 + 24 = 44 = 1

So on average, the numbers are 1 away from the mean.

4 Check

Let's check: the distances below the mean add up to 2.

Above the mean: 2.

The same, because the mean is the balance point.

So the distances are right!

below: 1.5 + 0.5 = 2, above: 2 = 2

Let's look back.

First: find the mean.

Then: distance from the mean.

Then: mean of the distances.

Last: check.

Answer