X is converted into a standard score by z = x − μ σ z=īecause student A has a higher z-score than student B, student A performed better compared to other test-takers than did student B. If the population mean and population standard deviation are known, a raw score

Ĭomputing a z-score requires knowledge of 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 using the sample mean and sample standard deviation yields the t-statistic. Other equivalent terms in use include z-value, z-statistic, normal score, standardized variable and pull in high energy physics. Standard scores are most commonly called z-scores the two terms may be used interchangeably, as they are in this article. This process of converting a raw score into a standard score is called standardizing or normalizing (however, 'normalizing' can refer to many types of ratios see Normalization for more). It is calculated by subtracting the population mean from an individual raw score and then dividing the difference by the population standard deviation. Raw scores above the mean have positive standard scores, while those below the mean have negative standard scores.

In statistics, the standard score is the number of standard deviations by which the value of a raw score (i.e., an observed value or data point) is above or below the mean value of what is being observed or measured. Comparison of the various grading methods in a normal distribution, including: standard deviations, cumulative percentages, percentile equivalents, z-scores, T-scores For other uses, see Z-score (disambiguation).

Standard normal table with Z score