Statistics and Probability Glossary
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z Score
A z-score (aka, a standard score)
indicates how many
standard deviations
an element is from the mean. A z-score can be
calculated from the following formula.
z = (X - μ) / σ
where z is the z-score, X is the value of the element, μ is the population
mean, and σ is the standard deviation.
Here is how to interpret z-scores.
- A z-score less than 0 represents an element less than the mean.
- A z-score greater than 0 represents an element greater than the mean.
- A z-score equal to 0 represents an element equal to the mean.
-
A z-score equal to 1 represents an element that is 1 standard
deviation greater than the mean; a z-score equal to 2, 2
standard deviations greater than the mean; etc.
-
A z-score equal to -1 represents an element that is 1 standard
deviation less than the mean; a z-score equal to -2, 2
standard deviations less than the mean; etc.
-
If the number of elements in the set is large, about 68% of the
elements have a z-score between -1 and 1; about 95% have a
z-score between -2 and 2; and about 99% have a z-score between
-3 and 3.
Here is another way to think about z-scores. A z-score is
the
normal random variable
of a
standard normal distribution
.
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