Question

SAT scores have a mean of 1026 and a standard deviation of 209. ACT scores have a mean of 20.8 and a standard deviation of 4.8. A student takes both tests while a junior and scores 860 on the SAT and 16 on the ACT. Compare the scores.

Answer 1

The z-score for SAT exam of junior is much small than his ACT score. This means he performed well in his ACT exam and performed poor in his SAT exam.

Explanation:

Mean SAT scores = 1026

Standard Deviation = 209

Mean ACT score = 20.8

Standard Deviation = 4.8

We are given SAT and ACT scores of a student and we have to compare them. We cannot compare them directly so we have to Normalize them i.e. convert them into such a form that we can compare the numbers in a meaningful manner. The best way out is to convert both the values into their equivalent z-scores and then do the comparison. Comparison of equivalent z-scores will tell us which score is higher and which is lower.

The formula to calculate the z-score is:

`z=(x-\mu)/(\sigma)`

Here, μ is the mean and σ is the standard deviation. x is the value we want to convert to z score.

z-score for junior scoring 860 in SAT exam will be:

`z=(860-1026)/(209)=-7.59`

z-score for junior scoring 16 in ACT exam will be:

`z=(16-20.8)/(4.8)=-1`

The z-score for SAT exam of junior is much small than his ACT score. This means he performed well in his ACT exam and performed poor in his SAT exam.