Z-Score Calculator
Calculate the number of standard deviations a data point is from the mean of a dataset. Enter your values below to find the z-score and its interpretation.
Understanding Z-Scores
A z-score (also called a standard score) indicates how many standard deviations away from the mean a data point is. It allows you to compare data points from different normal distributions.
How to Interpret Z-Scores
• A z-score of 0 means the data point equals the mean
• A positive z-score indicates the data point is above the mean
• A negative z-score indicates the data point is below the mean
• About 68% of the data falls within ±1 standard deviation
• About 95% falls within ±2 standard deviations
• About 99.7% falls within ±3 standard deviations
Z-Score Formula
The formula for calculating a z-score is:
z = (x - μ) / σ
Where:
• x is the value to be standardized
• μ (mu) is the population mean
• σ (sigma) is the population standard deviation
Common Applications
Z-scores are widely used in:
• Educational testing and grading
• Quality control in manufacturing
• Financial analysis and risk assessment
• Medical research and diagnostics
• Psychological testing and assessment