Z Score Review

A Z-score indicates how many standard deviations an element is from the mean of a data set.

A negative Z-score indicates that the score is below the mean.

A positive Z-score indicates that the score is above the mean.

The formula for calculating a Z-score is $$z=\frac{x-\text{mean}}{\text{SD}}$$ .

$$z=\frac{70-75}{5}=-1.0$$ .

A Z-score of 0 means the score is exactly at the mean.

A Z-score of +2 means the score is 2 standard deviations above the mean.

A Z-score of -2 means the score is 2 standard deviations below the mean.

$$z=\frac{60-50}{10}=1.0$$ .

$$z=\frac{45-50}{5}=-1.0$$ .