A person scores 81 on a test of verbal ability and 6.4 on a test of quantitative ability. For the verbal ability test, the mean for people in general is 50 and the standard deviation is 20. For the quantitative ability, the mean for people in general is 0 and the standard deviation is 5. Which is this person’s stronger ability: verbal or quantitative? Explain your answer to a person who has never had a course in statistics.

Question

A person scores 81 on a test of verbal ability and 6.4 on a test of quantitative ability.  For the verbal ability test, the mean for people in general is 50 and the standard deviation is 20.  For the quantitative ability, the mean for people in general is 0 and the standard deviation is 5.  Which is this person’s stronger ability: verbal or quantitative?  Explain your answer to a person who has never had a course in statistics.

PsyDAG · Answer

Z score is the raw score in terms of standard deviations from the mean. The Z score cuts off the same proportion for any normal distribution.

Z = (score-mean)/SD

Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion/probability for each Z score.