Mean, Median and Standard Deviation Explained
The core statistics everyone should know — mean, median, mode, range and standard deviation — what each tells you, when averages mislead, and how the normal distribution ties them together.
Z-Score Calculator
Verified formula Updated Jun 2026 Private — runs on your device
Verified formula
Private
Z-score
1.5000
For general information only — not financial, tax, legal or medical advice. Verify before you rely on it.
How to use the Z-Score Calculator
The Z-Score Calculator works out your z-score in an instant. Enter value (x), mean (μ) and standard deviation (σ) and the result updates as you type — it is free, needs no sign-up, and runs entirely in your browser so your figures stay private.
- Enter the value (x).
- Enter the mean (μ).
- Enter the standard deviation (σ).
- Read off your z-score — the calculator updates automatically, with no button to press.
Formula
The Z-Score Calculator uses the formula:
Z-score = (Value (x) - Mean (μ)) ÷ Standard deviation (σ)
Worked example
For example, with value (x) of 85, mean (μ) of 70 and standard deviation (σ) of 10, the z-score is 1.5000.
| Value (x) | 85 |
|---|---|
| Mean (μ) | 70 |
| Standard deviation (σ) | 10 |
| Z-score | 1.5000 |
|---|
Results are estimates for educational use, not professional advice.
Key terms explained
- Standard deviation
- A measure of how spread out a set of values is around their mean.
- Mean
- The average of a set of numbers — their sum divided by how many there are.
- Z-score
- How many standard deviations a value lies above or below the mean.
Frequently asked questions
A z-score tells you how many standard deviations a value is above or below the mean. A value of 85 with mean 70 and standard deviation 10 has a z-score of 1.5.
It means the value is below the mean. A z-score of 0 sits exactly at the mean, and positive scores are above it.
They put values from different distributions on the same scale, making it easy to compare and to find probabilities using the normal distribution.
Values beyond about ±2 are often considered unusual, and beyond ±3 are rare, since most data falls within three standard deviations of the mean.
The Z-Score Calculator uses the formula: Z-score = (Value (x) - Mean (μ)) ÷ Standard deviation (σ). For example, with value (x) of 85, mean (μ) of 70 and standard deviation (σ) of 10, the z-score is 1.5000.
Enter the value (x). Enter the mean (μ). Enter the standard deviation (σ). Read off your z-score — the calculator updates automatically, with no button to press.
Related guides
Z-Score Table: Z-score by Value (x)
Reference table of z-score for Z-Score across a range of value (x) values — exact, engine-computed figures you can read off at a glance.
How to Calculate Z-Score: Formula, Steps & Examples
Learn how to calculate Z-Score — the formula explained step by step, with worked examples and a free calculator to check your answer.