Statistics

 the formula to compute a z-score is:

Z = (value in pop - pop mean) / standard deviation

the resulting value of a z-score should be looked up in a Z-Score chart (http://www.regentsprep.org/Regents/math/algtrig/ATS7/ZChart.htm)

Expressed as a ratio from 0 to 1.00.   Observed in a distribution of scores to the maximum variation that could exist in a particular distribution.

 0.00 indicates no variation.  1.00 represents maximum variation.

 The most common usage for this is for nominal variables and it can be used with any variable when scores have been grouped into a frequency distribution.

For example, given the following tables representing a city's marital status in the hundreds, we may want to know which of the two cities is more diverse (or heterogeneous).

Tje z-score is often called the standardized value.  The standardized value or z-score can be interpreted as the number of standard deviations from the mean. 

So if x1 has a value of 4 and a z-score of 1.5, this would mean that 7 is 1.5 standard deviations more than the sample mean (goes right). 

Alternatively if x2 is equal to 1 and has a z-score of -1.3, this means that 1 is 1.3 standard deviations less than the sample mean (goes left).

Calculation:

z = (value in sample - sample mean) / standard deviation of sample