Z-score / Standard score

This is a small calculator to compute the standard score for a given data point. In statistics, the standard score 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.

Standard scores are also called z-values, z-scores, normal scores, and standardized variables.

The standard score of a raw score x is

where:

μ is the mean of the population.
σ is the standard deviation of the population.

The absolute value of z represents the distance between the raw score and the population mean in units of the standard deviation. z is negative when the raw score is below the mean, positive when above.

The key point is that calculating z requires the population mean and the population standard deviation, not the sample mean or sample deviation. It requires knowing the population parameters, not the statistics of a sample drawn from the population of interest.¹

Z-score / Standard score

Raw score

Mean

Deviation

Calculation precision

Digits after the decimal point: 2

Calculate

Z-score

 

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