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

Step by step

The question

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

5, 5, 5, 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 20.

There are 4 numbers.

20 divided by 4 is 5.

= mean = 5 + 5 + 5 + 54 = 204 = 5

2 Distance from the mean

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

5 is 0 away from 5: 5 minus 5.

5 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 0.

0 divided by 4 is 0.

= MAD = 0 + 0 + 0 + 04 = 04 = 0

So on average, the numbers are 0 away from the mean.

4 Check

Let's check: the distances below the mean add up to 0.

Above the mean: 0.

The same, because the mean is the balance point.

So the distances are right!

below: = 0, above: = 0

Let's look back.

First: find the mean.

Then: distance from the mean.

Then: mean of the distances.

Last: check.

Answer