Z-Score Value Calculator
Calculate the standard score to determine how many standard deviations a value is from the mean.
What is a Z-Score?
A Z-score, also known as a standard score, is a statistical measurement that describes a value's relationship to the mean of a group of values. It is measured in terms of standard deviations from the mean. If a Z-score is 0, it indicates that the data point's score is identical to the mean score. A Z-score of 1.0 would indicate a value that is one standard deviation from the mean.
How to Interpret the Result
- Positive Z-score: The raw score is higher than the mean average.
- Negative Z-score: The raw score is lower than the mean average.
- Z-score of 0: The raw score is exactly equal to the mean.
- Magnitude: A score of 2.0 or higher (or -2.0 or lower) is typically considered statistically significant or an outlier in many distributions.
Practical Example
Imagine a class takes a test where the mean (μ) is 75 and the standard deviation (σ) is 10. If a student scores an 85 (x), their Z-score calculation would be:
Z = (85 – 75) / 10 = 1.0
This means the student scored exactly one standard deviation above the class average.
Why Use a Z-Score Calculator?
Standardizing scores allows statisticians and researchers to compare data from different samples or populations that may have different scales. For instance, you can compare a student's performance on an SAT math section with their performance on an English essay by converting both to Z-scores, even though the raw scoring systems are completely different.