MAD of 30, 32, 35, 38, 40 Step by Step | Mean absolute deviation

Step by step

The question

Question: find the mean absolute deviation, the MAD, of 30, 32, 35, 38, 40.

30, 32, 35, 38, 40

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 175.

There are 5 numbers.

175 divided by 5 is 35.

= mean = 30 + 32 + 35 + 38 + 405 = 1755 = 35

2 Distance from the mean

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

30 is 5 away from 35: 35 minus 30.

32 is 3 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 16.

16 divided by 5 is 3.2.

= MAD = 5 + 3 + 0 + 3 + 55 = 165 = 3.2

So on average, the numbers are 3.2 away from the mean.

4 Check

Let's check: the distances below the mean add up to 8.

Above the mean: 8.

The same, because the mean is the balance point.

So the distances are right!

below: 5 + 3 = 8, above: 3 + 5 = 8

Let's look back.

First: find the mean.

Then: distance from the mean.

Then: mean of the distances.

Last: check.

Answer