Z-Score Calculator
Calculate standard scores to understand how a data point relates to the mean of a distribution
Calculate Z-Score
Z-Score Result:
0.00
This z-score indicates that your data point is exactly at the mean.
Mean (μ)
Your Data Point
Understanding Z-Scores
Z = (X - μ) / σ
A z-score (standard score) represents the number of standard deviations a data point is from the mean of a distribution.
Interpretation Guide:
- Z = 0: The data point is exactly at the mean
- |Z| < 1: The data point is within 1 standard deviation of the mean (common values)
- 1 < |Z| < 2: The data point is between 1-2 standard deviations from the mean (unusual values)
- |Z| > 2: The data point is more than 2 standard deviations from the mean (rare values)
- |Z| > 3: The data point is more than 3 standard deviations from the mean (very rare values)
Real-World Examples:
Test Scores: If a class average is 75 with standard deviation of 10, a score of 85 has a z-score of 1.0 (1 SD above mean).
Height: If average male height is 70" with SD of 3", a 79" tall man has a z-score of 3.0 (very tall).
Finance: Z-scores are used in stock analysis to identify overbought or oversold conditions.
Why Use Z-Scores?
- Compare data from different distributions
- Identify outliers in datasets
- Standardize data for machine learning
- Calculate probabilities in normal distributions
- Understand relative standing within a group