Similarly, if the Z-score is positive 2.5 means the value (x) is 2.5 standard deviations to the right of the mean (µ).
For example, if a Z-score is negative 3 means the value (x) is 3 standard deviations left of the mean. This is also called standardization.Ī Z-score tells how much standard deviation a value or score is from the mean (µ). Hence, use Z Scores to transform a given standard distribution into something that is easy to calculate probabilities on as it can determine the likelihood of some event happening.Īny normal distribution with any value of mean (µ) and a sigma can be transformed into the standard normal distribution, where the mean of zero and a standard deviation of 1. Each number on the horizontal line corresponds to z-score. The standard normal distribution is a type of special normal distribution with a mean (µ) of 0 and a standard deviation of 1.Ī standard normal distribution always has a mean of zero and has intervals that increase by 1. What is a Standard Normal Distribution?Ī Normal Standard Distribution curve is a symmetric distribution where the area under the normal curve is 1 or 100%. Similarly, if the Z value is negative, it means the value (x) is below the mean. If the Z value is positive, it indicates that the value or score (x) is above the mean. Technically, a Z-score tells you how many standard deviations value (x) is below or above the population mean (µ). In other words, the Z-score measures the dispersion of data.
Z scores (Z value) is the number of standard deviations a score or a value (x) is away from the mean.
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