Standard Scores


standard score

Score minus mean divided by standard deviation
Standard Score is variable without dimensions
it describe the relative position of single observation in compare to the distribution
it will be possible to compare different distributions

for example

in medical research the researcher check the blood sugar level
certain population

X - sugar level in milligram
Y - age
mean sugar 140
mean age 65
standard deviation sugar 40
standard deviation age 10
certain tested
age 72
sugar 155
what is relative condition in comparison to the rest of the population

0.375 = 40 / (155-140) = Zx
0.7 = 10 / (72-65) = Zy


the conclusion is


according the result his sugar level is higher then the mean in the population
his age is higher then the mean in the population
the age is more far from the mean age of the population
than the sugar level from the mean sugar of the population



the property of the Standard Score

Zx < 0 - the data is smaller then the mean

Zx = 0 - the data is equal to the mean

Zx > 0 - the data is bigger then the mean

the property of the Standard Score  mean equal zero   standard deviation equal one  







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