What do Z-Scores do?

What do Z-Scores do?

• A. They transform scores into ranks.
• B. They indicate the most frequent score.
• C. Z-Scores allow us to determine the raw score's location in a distribution, its relative frequency, and its percentile.
• D. They provide the mean and standard deviation of the distribution.

Answer: (C)

Z-scores standardize a raw score by expressing how many standard deviations it lies from the mean, and in which direction. This creates a common scale so you can compare scores across different distributions. With a Z-score, you can read three things: where the score sits relative to the center of the distribution (location in standard deviation units), how likely it is to occur in the distribution (the relative position shown by the area under the standard normal curve to the left of that Z), and the corresponding percentile (the rank of the score within the distribution). For example, a score 1.5 standard deviations above the mean has a Z of +1.5 and corresponds to about the 93rd percentile, meaning it’s higher than roughly 93% of scores. Z-scores aren’t about turning scores into ranks, nor do they indicate the most frequent score; they rely on the mean and standard deviation to express position, and those values are needed to compute the Z itself.

Z-scores standardize a raw score by expressing how many standard deviations it lies from the mean, and in which direction. This creates a common scale so you can compare scores across different distributions. With a Z-score, you can read three things: where the score sits relative to the center of the distribution (location in standard deviation units), how likely it is to occur in the distribution (the relative position shown by the area under the standard normal curve to the left of that Z), and the corresponding percentile (the rank of the score within the distribution). For example, a score 1.5 standard deviations above the mean has a Z of +1.5 and corresponds to about the 93rd percentile, meaning it’s higher than roughly 93% of scores. Z-scores aren’t about turning scores into ranks, nor do they indicate the most frequent score; they rely on the mean and standard deviation to express position, and those values are needed to compute the Z itself.