The Z-Score Calculator finds the standard score of a value relative to the mean and standard deviation of a data set. A z-score tells you how many standard deviations above or below the mean a particular value lies.
This is a fundamental concept in statistics, widely used in education, testing, finance, and science.
What does the calculator do?
- Enter raw score (x): The value you want to standardise.
- Enter mean (μ) and standard deviation (σ) of the data set.
- Calculate z-score: Using the formula
- Copy result: One click to paste into homework, notes, or reports.
Worked examples
Example 1 — Test scores
- Raw score = 85
- Mean = 70
- Standard deviation = 10
z=(85−70)/10=1.5
Result: The score is 1.5 standard deviations above the mean.
Example 2 — Below the mean
- Raw score = 55
- Mean = 70
- Standard deviation = 10
z=(55−70)/10=−1.5
Result: The score is 1.5 standard deviations below the mean.
Example 3 — Heights in a population
- Height = 190 cm
- Mean = 175 cm
- Standard deviation = 5 cm
z=(190−175)/5=3
Result: This height is 3 standard deviations above average, showing it’s unusually tall.
Why is it important?
- In school: Z-scores connect data values to the standard normal distribution, paving the way to probability calculations.
- In testing: Used to compare exam scores across different tests.
- In science: Helps identify outliers and unusual observations.
- In finance: Z-scores detect anomalies in stock prices, credit risk, and more.
Frequently Asked Questions
Q1: What does a negative z-score mean?
It means the value is below the mean.
Q2: What does a z-score of 0 mean?
It means the value is exactly at the mean.
Q3: How do I interpret a high z-score?
The further from 0, the more unusual the value. For example, ±2 is already quite rare in a normal distribution.
Q4: Why divide by the standard deviation?
This standardises the data, so scores can be compared across different scales.