Standard Deviation & Z-Scores

Standard Deviation is a measure of the amount of variation or dispersion in a set of values. A low standard deviation means that the values tend to be close to the mean, while a high standard deviation means that the values are spread out over a wider range.

A Z-Score indicates how many standard deviations an element is from the mean. It is calculated by subtracting the mean from the value and then dividing by the standard deviation.

Z-Score = (Value - Mean) / Standard Deviation.

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.

Z-Score = (65 - 50) / 10 = 1.5.

Z-Score = (45 - 40) / 5 = 1.

A standard deviation of 0 means there is no spread of data; all values are identical.

The Z-Score would be -2.00.