Question

Find or make up a small set of scores. Demonstrate the steps you'd go through to transform all of the scores into z-scores. As a variation, demonstrate how you'd transform the distribution of z-scores into a different standardized distribution with a mean other than 0 & an SD different from 1.

Answer 1

Below are 8 random numbers

x
27
43
34
47
23
40
34
52

Z = (X - mean)/sd

here

mean = 37.5

sd = 9.8706

hence

Z = (X - 37.5)/9.8706

x	z-score
27	-1.06377
43	0.557211
34	-0.35459
47	0.962455
23	-1.46901
40	0.253278
34	-0.35459
52	1.46901

X = mean + z * sd

suppose we want to convert this in different standardized distribution with mean = 100 and sd = 20 {say}

hence

X = 100 + z * 20

new scores Y would be

x	z-score	Y
27	-1.06377	78.72468
43	0.557211	111.1442
34	-0.35459	92.90823
47	0.962455	119.2491
23	-1.46901	70.61979
40	0.253278	105.0656
34	-0.35459	92.90823
52	1.46901	129.3802

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