Which statement best distinguishes percentile rank from a z-score?

Which statement best distinguishes percentile rank from a z-score?

• A. Percentile rank is a position relative to the population; z-score is deviation from the mean in standard deviation units.
• B. Percentile rank is always more precise than a z-score.
• C. Z-score provides a probability; percentile does not.
• D. Z-score is used only for measurement error.

Answer: (A)

Percentile rank and a z-score measure different things about a score. A percentile rank tells you where a score sits in the population as a percentage—how much of the population scores at or below that value. A z-score, on the other hand, tells you how far the score is from the mean, measured in units of standard deviation. It’s a standardized distance from the center of the distribution, not a direct position. These ideas are related but not the same: a score at the 90th percentile means you’re higher than 90% of people, while a z-score of +1.28 (in a normal distribution) roughly corresponds to that same position, but expressed as a distance from the mean in standard deviation units. The z-score provides a precise, scale-free measure of deviation, whereas the percentile conveys rank relative to the entire population. The other statements mix up these distinctions: a percentile isn’t inherently less precise or more precise than a z-score in a general sense, a z-score isn’t itself a probability (though it can be used to find one in the standard normal distribution), and z-scores aren’t used only for measurement error.

Percentile rank and a z-score measure different things about a score. A percentile rank tells you where a score sits in the population as a percentage—how much of the population scores at or below that value. A z-score, on the other hand, tells you how far the score is from the mean, measured in units of standard deviation. It’s a standardized distance from the center of the distribution, not a direct position.

These ideas are related but not the same: a score at the 90th percentile means you’re higher than 90% of people, while a z-score of +1.28 (in a normal distribution) roughly corresponds to that same position, but expressed as a distance from the mean in standard deviation units. The z-score provides a precise, scale-free measure of deviation, whereas the percentile conveys rank relative to the entire population.

The other statements mix up these distinctions: a percentile isn’t inherently less precise or more precise than a z-score in a general sense, a z-score isn’t itself a probability (though it can be used to find one in the standard normal distribution), and z-scores aren’t used only for measurement error.