Zvalues
A z-value, also called a z-score or standard score, is a measure of how many standard deviations an individual observation is from the mean of a population. The standard formula is z = (X − μ) / σ, where X is the observed value, μ is the population mean, and σ is the population standard deviation. The concept can be applied to samples as z = (X − x̄) / s, using the sample mean x̄ and sample standard deviation s.
In theory, when the underlying variable is normally distributed with mean μ and standard deviation σ, the z-values
Z-values have several common applications. In hypothesis testing, test statistics based on z, such as Z =
Beyond inferential statistics, z-scores are widely used to standardize data for comparability, transforming different variables to
Important caveats include that the exact probabilities tied to z-values assume normality and known σ. When σ is