Mean signed deviation

So you know how sometimes we have to find the middle of a bunch of numbers? That's called the "average" or "mean". But sometimes we also want to see how far away each number is from the middle. That helps us understand if the numbers are all really close together or if they are spread out far apart.

That's where something called "mean signed deviation" comes in. It's like looking at each number and asking "how far away are you from the average?" But instead of just giving a distance, it also says whether you are above or below the average.

Let's say we have a bunch of numbers: 3, 6, 9, 12, and 15. The average is 9. So let's see how much each number is different from that average:

- 3 is six less than the average
- 6 is three less than the average
- 9 is the same as the average
- 12 is three more than the average
- 15 is six more than the average

Now we add up all those differences, but we ignore the signs (+ or -), because we want to see how big the differences are on average.

We get:

(6 + 3 + 0 + 3 + 6) / 5 = 18 / 5 ≈ 3.6

So the mean signed deviation is about 3.6. That means, on average, each number is about 3.6 away from the middle. But we also know which direction it is in, because of the signs.