Differentiate percentile rank from z-score.

Differentiate percentile rank from z-score.

• A. Percentile rank indicates relative standing within a distribution; z-score indicates how many standard deviations a score is from the mean.
• B. Z-score indicates relative standing; percentile indicates standard deviation.
• C. Both are the same.
• D. Percentile rank indicates how many standard deviations from the mean.

Answer: (D)

Percentile rank tells you where a score sits in the distribution in terms of relative position. It’s the percentage of scores that are at or below that value, so it’s about ranking and standing within the group, not about distance from the mean. A z-score, by contrast, standardizes a score by expressing its distance from the mean in units of the standard deviation. It shows how many standard deviations away from the mean the score lies and in which direction (positive above the mean, negative below). So they measure different things: percentile rank is about relative position within the distribution; z-score is about how far and in what direction the score is from the mean, in standard deviation units. In a normal distribution you can relate the two, but conceptually they’re not the same.

Percentile rank tells you where a score sits in the distribution in terms of relative position. It’s the percentage of scores that are at or below that value, so it’s about ranking and standing within the group, not about distance from the mean.

A z-score, by contrast, standardizes a score by expressing its distance from the mean in units of the standard deviation. It shows how many standard deviations away from the mean the score lies and in which direction (positive above the mean, negative below).

So they measure different things: percentile rank is about relative position within the distribution; z-score is about how far and in what direction the score is from the mean, in standard deviation units. In a normal distribution you can relate the two, but conceptually they’re not the same.