Statistics Tool
Z-Score Calculator
Calculate the Standard Score (Z-Score) for a normal distribution.
Z-Score
2.0000
Above Average
Σ The Formula
Z = (x - μ) / σ
Real World Examples
Example
x=85, μ=75, σ=5 → Z=2.0
# About This Calculator
A Z-score describes a value's relationship to the mean of a group of values. It is measured in terms of standard deviations from the mean.
- Z = 0: The score is exactly the mean.
- Positive Z: The score is above the mean.
- Negative Z: The score is below the mean.
Frequently Asked Questions
What is a Z-Score?+
A Z-score tells you how many standard deviations a data point is away from the mean.
How do I interpret a Z-Score?+
0 is exactly average. +2.0 is very high (top 2.5%). -2.0 is very low (bottom 2.5%).
What is the Z-Score formula?+
Z = (X - μ) / σ. (Value - Mean) divided by Standard Deviation.
Why are Z-Scores useful?+
They let you compare 'apples to oranges'. You can compare a test score in Math vs English to see which one was relatively better.
How does this relate to p-values?+
Every Z-score corresponds to a specific p-value (probability) on the Standard Normal Distribution table.
What is a 'Standard Normal Distribution'?+
It is a normal distribution where the Mean is 0 and the Standard Deviation is 1.
About
A Z-score describes a value's relationship to the mean of a group of values. It is measured in terms of standard deviations from the mean.
- Z = 0: The score is exactly the mean.
- Positive Z: The score is above the mean.
- Negative Z: The score is below the mean.