Raw scores on behavioral tests are often transformed for easier comparison. A te
ID: 3272911 • Letter: R
Question
Raw scores on behavioral tests are often transformed for easier comparison. A test of reading ability has mean 52 and standard deviation 5 when given to third graders. Sixth graders have mean score 81 and standard deviation 7 on the same test. To provide separate "norms" for each grade, we want scores in each grade to have mean 100 and standard deviation 20. (Round your answers to two decimal places.) (a) What linear transformation will change third-grade scores x into new scores xnew = a + bx that have the desired mean and standard deviation? (Use b > 0 to preserve the order of the scores.)
Explanation / Answer
Answer:
Given that,
Third grades: mean = 52
standard deviation = 5
sixth grades: mean = 81
standard deviation = 7
new grades: mean = 100
standard deviation = 20
and also given that:
Xnew = a+bx
=> Snew = bs
=> 20 = b(5)
=> b = 20/5
.'. b = 4
=> a = Xnew-b(x)
= 100-4(52)
= 100-208
= -108
.'." Xnew = -108+4x "
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