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# Standard score

In statistics, a standard score (z) is a dimensionless quantity derived by subtracting the mean score of a probability distribution from an individual score and then dividing the difference by the standard deviation:

$z = {X - \overline{X} \over s}$

The quantity z is the number of standard deviations between the score and the mean; it is negative when the raw score is below the mean. The conversion allows the comparison and combination of measures made on different scales. If data are being combined or scaled the conversion eliminates accidental weighting due to differences in means or standard deviations. Standard scores are chiefly appropriate for data that are normally distributed. The standard score also provides an estimate of the percentile rank of scores in a normal distribution.

A standard score is a way of placing a raw score in context. It is often used to compare test results within and between groups, and especially with reference to a norm group.

• Examples (http://soeweb.syr.edu/faculty/ddgilbri/assess/StandardScores)

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