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Z-Score Calculator
You can use this Z-Score Calculator to calculate the standard normal score (z-score) based on the raw score value, the population mean, and the standard deviation of the population.
How to use the calculator
- Enter the raw score value
- Enter the mean, standard deviation, and click the "Calculate" button to see the results.
Results
Z-Score: 2.5
The Z-score (z) is calculated according to the formula: z = (x - μ) / σ
Where: x is the raw score value, μ is the mean of the population, σ is the standard deviation of the population.
x = 15, μ = 5, σ = 4
z = (15 - 5) / 4
z = 10 / 4 = 2.5
Z-score is 2.5
Where: x is the raw score value, μ is the mean of the population, σ is the standard deviation of the population.
x = 15, μ = 5, σ = 4
z = (15 - 5) / 4
z = 10 / 4 = 2.5
Z-score is 2.5
Z-Score Formula
The Z-Score Calculator uses the following formula:
z = (x - μ) / σ
Where:
z is the standard score or Z-score,
x is the raw score to be standardized,
μ is the mean of the population,
σ is the standard deviation of the population.
Z-Score Calculation Example
The mean of a dataset is 20 and the standard deviation is 7. Find the z-score for a value of 6.
x = 6, μ = 20, σ = 7
z = (6 - 20) / 7
z = -14 / 7 = -2
z = -2
Reference: Norman, G. R. and Streiner, D. L., Biostatistics: The Bare Essentials. 2nd edition. London: B.C. Decker, 2000.