How we change what others think, feel, believe and do
Thus z is a measure of how far away a measurement is from the mean, measured in standard deviations.
z = (X - X-bar)/S
Where X is a measured value, X-bar is the mean of all measured values and S is the standard deviation of all measured values.
John gets a mark of 64 in a physics
Jane gets a mark of 74 in a chemistry test, where the mean is
58 and the
John's z = (64 - 50) / 8 = 1.75
Jane's z = (74 - 58) / 10 = 1.6
Although Jane's score is higher, John's score is further above the mean, and it might be concluded that John has achieved greater success.
The z-score provides a simple measure by which different measures can be compared in terms of their deviation from the mean. This is often called standardization.
The z-score in use generally assumes parametric data.