Use Tom’s ACT score, 24, along with the ACT mean and standard deviation to compute his Z-score.
x <- 24 # Observation
m <- 21 # Mean
sd <- 5 # Standard Deviation
z <- (x - m)/sd
z
[1] 0.6
Observations above the mean always have positive Z-scores while those below the mean have negative Z-scores. If an observation is equal to the mean, then the Z-score is 0.
