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
where:
- 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!
Summary
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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Prefer to read in Polish? Here’s the translation of this article.
