Z-Score Calculator
Your Z-Score is:
0.00
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.
The Formula for Calculating Z-Score
To calculate a Z-score, you subtract the population mean from the individual raw score and then divide the result by the population standard deviation.
Z = (x – μ) / σ
- x: The raw score or value being measured.
- μ: The population mean (average).
- σ: The population standard deviation.
How to Interpret the Result
The resulting Z-score tells you exactly where your score lies on a normal distribution curve:
- Positive Z-score: The value is above the average.
- Negative Z-score: The value is below the average.
- Z-score of 0: The value is exactly equal to the average.
Real-World Example
Imagine a student scores 85 on a math test. The class average (mean) was 75, and the standard deviation was 10. Using the formula:
Z = (85 – 75) / 10 = 10 / 10 = 1.00
This means the student's score is 1 standard deviation above the mean.