z-scores are referred to as "standard scores" because irrespective of the size and unit of X values the corresponding z-scores can be obtained to determine the proportion or probability concerned.
It is just like a percentage or a ratio or a fraction.
The total area under the standard normal curve = 1 and the z-score enables us to determine the area representing the probability.
The probability or proportion corresponding to a certain z-score is determined by
i) consulting a z-scores chart/table or
ii) using a graphic calculator.
for ex. If mean of a variable = 100,000 and Standard deviation = 20,000
the z value corresponding to X = 50,000 is (X-Mu)/SD = (100,000-50,000)/20,000 = + 2.5
If mean of another variable = 40 and SD = 8
the z value corresponding to X = 20 is (40-20)/8 = + 2.5
If the unit of a variable is kilograms and that of another variable is hours there will not be any change in the standardisation.
It is just like a percentage or a ratio or a fraction.
The total area under the standard normal curve = 1 and the z-score enables us to determine the area representing the probability.
The probability or proportion corresponding to a certain z-score is determined by
i) consulting a z-scores chart/table or
ii) using a graphic calculator.
for ex. If mean of a variable = 100,000 and Standard deviation = 20,000
the z value corresponding to X = 50,000 is (X-Mu)/SD = (100,000-50,000)/20,000 = + 2.5
If mean of another variable = 40 and SD = 8
the z value corresponding to X = 20 is (40-20)/8 = + 2.5
If the unit of a variable is kilograms and that of another variable is hours there will not be any change in the standardisation.