MAD of 1, 3, 5 Step by Step | Mean absolute deviation

Step by step

The question

Question: find the mean absolute deviation, the MAD, of 1, 3, 5.

1, 3, 5

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 9.

There are 3 numbers.

9 divided by 3 is 3.

= mean = 1 + 3 + 53 = 93 = 3

2 Distance from the mean

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

1 is 2 away from 3: 3 minus 1.

3 is 0 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 4.

4 divided by 3 is about 1.3.

= MAD = 2 + 0 + 23 = 43 ≈ 1.3

So on average, the numbers are 1.3 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: 2 = 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