What is a Z-score: A Friendly Guide to Standard Deviations

20 June 2023

What is a Z-score - Standard Deviations

Hello! Today we’re answering a question “What is a Z-score”. I other words, we’ll talk about an important aspect of statistics – standard deviations. If you’ve never heard of it before, don’t worry – this is the place where you’ll learn everything you need to know.

What is a Z-score?

So, what is a Z-score? It’s nothing more than a measure that shows how much a given value differs from the average. In other words, it’s a way to determine how “atypical” our value is compared to all others.

Sounds complicated? Not at all! Let’s take a specific example.

Standard Deviations example

Imagine we have a national standardized test. The average test score is 300 out of 500 points, and the standard deviation is 50 points. Now, one of the students got a perfect score, that is 500 points. How can we determine how “atypical” this score is? That’s where the Z-score comes in.

We calculate the Z-score using the following formula:

Z = (X – μ) / σ


  • Z is the Z-score, or the number of standard deviations by which our value differs from the mean.
  • X is the value we are comparing with the mean – in our case, the student’s score, which is 500.
  • μ is the average – here 300.
  • σ is the standard deviation – here 50.

We substitute our values into the formula:

Z = (500 – 300) / 50 = 200 / 50 = 4

This means that our student’s score is 4 standard deviations above the average. Wow, that’s really impressive!


As you can see, the Z-score is an incredibly useful tool in statistics. It gives us a quick and easy way to assess how much a given value differs from the “norm”. Roughly speaking, it shows us how much something is “normal” or “abnormal”.

I hope this post has helped you understand what a Z-score is. Remember, statistics don’t have to be difficult – just take it step by step!

That’s all on this topic. Analyze in peace!

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