MAD of 10, 12, 14, 16 Step by Step | Mean absolute deviation

Step by step

The question

Question: find the mean absolute deviation, the MAD, of 10, 12, 14, 16.

10, 12, 14, 16

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 52.

There are 4 numbers.

52 divided by 4 is 13.

= mean = 10 + 12 + 14 + 164 = 524 = 13

2 Distance from the mean

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

10 is 3 away from 13: 13 minus 10.

12 is 1 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 8.

8 divided by 4 is 2.

= MAD = 3 + 1 + 1 + 34 = 84 = 2

So on average, the numbers are 2 away from the mean.

4 Check

Let's check: the distances below the mean add up to 4.

Above the mean: 4.

The same, because the mean is the balance point.

So the distances are right!

below: 3 + 1 = 4, above: 1 + 3 = 4

Let's look back.

First: find the mean.

Then: distance from the mean.

Then: mean of the distances.

Last: check.

Answer