“Everybody’s different,” I told K8 the other day.

And now I’m prepping standard *z*-scores for the statistics part of Finite Math.

So I’m thinking about *how much* everybody’s different. Like really – the *actual amount* of different each person is.

### Standard *z*-Scores help us see this!

Let’s say “average” means you’re no different. So being above or below average means you’re different.

And since everybody’s different in *different things*, how do we measure just *how much different* each person is – overall?

I propose we can do this with standard *z*-scores.

Or we can at least teach standard *z*-scores with this analogy.

### Standard *z*-scores work in real life.

Let’s look at three qualities: smartness, friendliness and athleticism. Here’s our assumed numbers:

- The average smartness is 100, with a standard deviation of 21.
- The average friendliness is 23, with a standard deviation of 5.
- And the average athleticism is 842 with a standard deviation of 57.

Now let’s take three “different” people.

- Alice is super smart – she’s 132 in the smartness scale.
- Bert is very nice to people – he’s 27 in the friendliness scale.
- Charlie uses his brain more than his body – he’s 753 in the athleticism scale.

Each of these people are different in their own areas. But if we were going to measure *how* different they were – like who’s the most different – it would be hard.

Is Alice more different than Bert? How about Charlie?

And how can we tell?

### Standardizing their scores levels the playing field!

Using the standard *z*-score we can see how different each person is.

Here’s the formula:

*z* = (their score – average) ÷ standard deviation

So for each:

- Alice’s
*z*-score = (132 – 100) ÷ 21 = 1.52 - Bert’s
*z*-score = (27 – 23) ÷ 5 = 0.80 - Charlie’s
*z*-score = (753 – 842) ÷ 57 = – 1.56

Even though Charlie’s score is negative, the absolute value of it is more than either Bert’s standard score or Alice’s.

So Charlie is the most different!

### What is the standard *z*-score – really?

The Standard z-score is the number of standard deviations above the average something is. But when you say that, it doesn’t make much sense. At least until you have a feel for what that could mean in real life.

You can use this real life example (although less “real” than “life”) to show students what the purpose of a z-score is. And why it’s not just some obscure statistical thing – like it seems!

### Your turn!

Will you use this when teaching statistics? Can you improve on it?

Share your thoughts in the comments – and wish me luck in my class today!

This post may contain affiliate links. When you use them, you support us so we can continue to provide free content!