Z-Scores

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

The Z-Score is calculated using the formula: $$z = \frac{{x - \text{mean}}}{{\text{standard deviation}}}$$ where x is the value, mean is the average of the data set, and standard deviation measures the spread of the data.

A Z-Score of 0 indicates that the value is exactly equal to the mean.

A positive Z-Score indicates that the value is above the mean.

A negative Z-Score indicates that the value is below the mean.

The Z-Score is $$z = \frac{{55 - 50}}{{5}} = 1.00$$ .

The Z-Score is $$z = \frac{{90 - 100}}{{10}} = -1.00$$ .

The Z-Score is -2.00.

It means the value is more than 2 standard deviations above the mean, indicating it is significantly higher than average.

It means the value is more than 2 standard deviations below the mean, indicating it is significantly lower than average.