Standard Score (Z-Score)
Standard Score (Z-Score)
\[z=\frac{x-\mu}{\sigma}\]
Variables
z = standard score
x = observed value
mu = population mean
sigma = population standard deviation
Description
What is this formula?
This formula calculates the standard score, also known as the z-score. It measures how many standard deviations a value is from the population mean.
When to use it
Use this formula to standardize data, compare values from different distributions, or identify unusual observations.
Example
If a test score is 85, the population mean is 70, and the standard deviation is 10, the z-score indicates how far the score is above average.
Applications
Statistics, quality control, finance, data analysis, machine learning, educational testing, and scientific research.
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