Question

IQ-scores are standard-score transformed scores having a mean of 100 and a standard deviation of 15; SAT scores are standard-score transformed scores having a mean of 500 and a standard deviation of 100. In what follows, X refers to a raw score from a distribution with a mean of X and a standard deviation of S, and SAT and IQ refer to the corresponding transform of that score. Solve for the missing value in each of the following:

(a) X=-2.5;Xmean= ;S=1;SAT=250

(b) X= ;Xmean=-12;S=12;IQ=130

(c) X=6;Xmean=12;S= ;SAT=450

(d) X=5;Xmean=-5;S=5;IQ=

(e) X=-7;Xmean=-1;S= ;IQ=25

I am having difficulties solving this. Do I multiply the deviation of the test scores by the formula to get a standard score?

Answer 1

(X - Xmea)/sd(X) = (S - Smean)/sd(S) = (IQ - mean(IQ))/sd(IQ)

a)

(-2.5 - Xmean)/1 = (250 - 500)/100

Xmean = 0

b)
(X + 12)/12 = (130 - 100)/15
X = 12
c)
(6 - 12)/S = (450 - 500)/100
S = 12

d)
(5 + 5)/5 = (IQ - 100)/15
IQ =130