Z-Score or Standard Score in statistics is the signed number of standard deviations by which the value of an observation or data point is above the mean value of what is being observed or measured. Observed values above the mean have positive standard scores, while values below the mean have negative standard scores. The standard score is a dimensionless quantity obtained by subtracting the population mean from an individual raw score and then dividing the difference by the population standard deviation. This conversion process is called standardizing or normalizing (however, “normalizing” can refer to many types of ratios). The score is most frequently used to compare an observation to a standard normal deviate, though it can be defined without assumptions of normality. Computing a z-score requires knowing the mean and standard deviation of the complete population to which a data point belongs, if one only has a sample of observations from the population, then the analogous computation with sample mean and sample standard deviation yields the Student’s t-statistic.

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