Z-Score Calculator: Free Standard Normal Distribution Tool
Z-Score Calculator
Calculate the standard score (Z-score) of a raw value given the population mean and standard deviation.
Z-SCORE RESULT
Z = 0.0000
Enter valid inputs to analyze distribution.
What is a Z-Score?
A **Z-score** (or standard score) represents how many standard deviations a given data point is away from the mean. If a Z-score is zero, it indicates that the data point's score is identical to the mean score. Positive Z-scores designate values above the mean, while negative Z-scores point to values below the mean. Our online **Z-Score Calculator** makes it effortless to compute standard scores for academic, financial, and scientific data analysis.
The Mathematical Formula
Computing a Z-score involves subtracting the population mean from the raw data value and dividing the result by the standard deviation.
Z-Score Formula:
$Z = \frac{x - \mu}{\sigma}$
Where: $x$ = Raw score, $\mu$ = Population mean, $\sigma$ = Standard deviation
$Z = \frac{x - \mu}{\sigma}$
Where: $x$ = Raw score, $\mu$ = Population mean, $\sigma$ = Standard deviation
Frequently Asked Questions (FAQ)
Q: What does a Z-score of +2.0 mean?
A: A Z-score of +2.0 means the observed value is two standard deviations above the average mean, placing it in the top tier of the normal distribution.
A: A Z-score of +2.0 means the observed value is two standard deviations above the average mean, placing it in the top tier of the normal distribution.
Q: Why are Z-scores important in statistics?
A: Z-scores allow analysts to compare data from completely different normal distributions and scales on a standardized uniform platform.
A: Z-scores allow analysts to compare data from completely different normal distributions and scales on a standardized uniform platform.
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