Standard Scores
A standard score (aka, a z-score) indicates how many standard deviations an element is from the mean. A standard 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 mean of the population, 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.
Let value of μ = M and value of σ = a
