Standard Scores

The standard score is the result of subtracting the direct scores from the arithmetic mean and then dividing them by the standard deviation. This process is called standardizing or normalizing.

The standard scores are denoted by z.

Standard Score Formula

Comments on Standard Scores

The arithmetic mean of a standard score is 0.

The standard deviation of a standard score is 1.

The standard scores are dimensionless, that is to say, they are independent of the units used.

The standard scores are used to compare the scores in different distributions.


In a class, there are 15 boys and 20 girls. The average weight of the male students is 58.2 pounds and 54.4 pounds for the female students. The standard deviations of the two groups are, respectively, 3.1 pounds and 5.1 pounds. Joseph´s weight is 70 pounds and Anne´s is 65 pounds. Which of them within their respective gender groups can be considered heavier?

Standard Score Example

Joseph is considered heavier with respect to his gender group.