Which score has the highest relative position: a score of 46 on a test for which $\bar { x } = 43$ and s $= 6$, a score of $4.3$ on a test for which $\bar { x } = 3.8$ and $s = 0.9$ or a score of $378.5$ on a test for which $\bar { x } = 351$ and $\mathrm { s } = 55 ?$
A) A score of 46
B) A score of 4.3
C) A score of 378.5

Question

Quizplus · Accepted Answer

The relative position is determined by the z-score, calculated as $ z = \frac{x - \bar{x}}{s} $. For each score:  A) $ z = \frac{46 - 43}{6} = 0.5 $  B) $ z = \frac{4.3 - 3.8}{0.9} \approx 0.56 $  C) $ z = \frac{378.5 - 351}{55} \approx 0.5 $  The score of 4.3 has the highest z-score, indicating the highest relative position.

Which Score Has the Highest Relative Position: a Score of 46