Z-Scores: Standardizing the World

How do you know if a 6ft man is "tall"? You compare him to the average. Z-Scores are the mathematical way to do that.

Check Your Score

Enter X, Mean, and SD to find Z.

Z-Score Calculator

The Formula

It is surprisingly simple. You just find the difference from the mean, and divide by the spread (Standard Deviation).

Z = (X - μ) / σ
  • X: The value you are testing.
  • μ (Mu): The Mean (Average).
  • σ (Sigma): The Standard Deviation.

Example: The Tall Friend

Let's say the average US male height is 69 inches with a Standard Deviation of 3 inches. Your friend is 6'3" (75 inches).

Calculation: (75 - 69) / 3 = 6 / 3 = 2.0

Your friend has a Z-Score of +2. This puts him in the 97.7th percentile. He is taller than ~98% of men.

Using Z-Tables

Once you have a Z-Score, you look it up in a "Standard Normal Distribution Table" (Z-Table) to find the exact probability or percentile. For example, a Z-Score of 1.96 corresponds to exactly 97.5% of the curve being to the left.

Z-Score FAQs

A Z-Score of 0 means the data point is exactly the same as the mean (average). It is right in the center of the bell curve.