ToolsArena.Net

Understanding Z-Scores and Standard Scores

A Z-score tells you how many standard deviations a data point is from the mean of its distribution. Z-scores allow you to compare values from different datasets with different scales. A Z-score of 0 means the value is exactly average. Positive Z-scores are above average, negative Z-scores are below.

Google ad

Formula

$$Z = \frac{x - \mu}{\sigma}$$

Z-Score Calculator

Calculate the Z-score (standard score) of a data point in a distribution.

Google ad

Worked Example

Given:

Data point (x) = 85Population mean (μ) = 70Standard deviation (σ) = 10
ResultZ-Score: 1.5 — Approximately 93rd percentile

Related Calculators

FAQs

What does a Z-score of 1.96 mean?

A Z-score of 1.96 corresponds to the 97.5th percentile of a standard normal distribution and is the critical value for a 95% confidence interval — 95% of values fall within ±1.96 standard deviations of the mean.

How do I interpret a negative Z-score?

A negative Z-score means the value is below the mean. A Z-score of -1 means the value is 1 standard deviation below average. About 16% of values in a normal distribution fall below a Z-score of -1.

What is the difference between a Z-score and a T-score?

Z-scores are used when the population standard deviation is known and sample size is large. T-scores are used when the standard deviation is unknown and must be estimated from the sample — the more common scenario with small samples.