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The z-score is a statistical transformation that specifies how far a particular value lies from the mean of a normal distribution in terms of standard deviations, z-scores are particularly helpful in comparing observations that come from different populations and from distributions with different means, standard deviations, or both. A z-score has meaning only if it is calculated for observations that are part of a normal distribution.

z-scores are sometimes referred to as standard scores. When the values of a normal distribution are transformed into z-scores, the transformed distribution is said to be “standardized” such that the new distribution has a mean equal to 0 and a standard deviation equal to 1.

The z-score for any observation is calculated by subtracting the population mean from the value of ...

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