Question

Math part of SAT test scores has mean μ=500 and standard deviation σ=100. ACT test scores have mean μ=18 and standard deviation σ=6. Eleanor scored 680 on her SAT math test, Frodo received score of 27 on his ACT test.

Assuming that both tests measured the same ability, who has a better score.

Answer 1

An Z score can be used to compared the scores having two different distributions.

Z = (X - )/

For Eleanor's SAT score, = 500

= 100

X = 680

Z = (680 - 500)/100 = 1.80

For Frodo's ACT score, = 18

= 6

X = 27

Z = (27 - 18)/6 = 1.5

The Z score is higher for the Eleanor's SAT score. Therefore, Eleanor has a better score.