Z-Score Calculator
Calculate standard scores and understand their significance
Calculator
Z-Score Result
0.00
The data point is exactly at the mean.
What is a Z-Score?
A Z-score (also called a standard score) measures how many standard deviations a data point is from the mean of a dataset. It's a statistical measurement that describes a value's relationship to the mean of a group of values.
Z = (X - μ) / σ
Where:
- Z is the Z-score
- X is the value being measured
- μ (mu) is the mean of the population
- σ (sigma) is the standard deviation of the population
Interpretation
A Z-score of 0 indicates the data point is exactly at the mean. A positive Z-score indicates the data point is above the mean, while a negative Z-score shows it's below the mean.
Examples
Z = 1.0: One standard deviation above the mean (84th percentile)
Z = -1.5: 1.5 standard deviations below the mean (6.7th percentile)
Z = 2.0: Two standard deviations above the mean (97.7th percentile)
Z = -2.0: Two standard deviations below the mean (2.3rd percentile)
Applications of Z-Scores
Z-scores are widely used in various fields including psychology, education, finance, and health. They allow for comparison of data points from different normal distributions and are fundamental in hypothesis testing, quality control, and risk management.
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