What is a z-score?

What is a z-score?

• A. The number of standard deviations away from the mean (positive above the mean) in a normal distribution
• B. The average value of a data set
• C. The range of the data
• D. The square root of the variance

Answer: (A)

A z-score shows where a value sits relative to the overall pattern, measured in standard deviation units. It tells you how many standard deviations away from the mean the value is, and whether it lies above or below the mean. You calculate it with z = (X − μ) / σ, which centers the data at zero and scales by the spread. This standardization lets you compare values from different distributions or scales because all z-scores map onto a common reference—the standard normal distribution with mean 0 and SD 1. Think of the other statistics as describing different things: the average is the central tendency, the range is the span from lowest to highest value, and the standard deviation is the average distance from the mean (a measure of dispersion). The z-score, in contrast, expresses that distance in units of standard deviation.

A z-score shows where a value sits relative to the overall pattern, measured in standard deviation units. It tells you how many standard deviations away from the mean the value is, and whether it lies above or below the mean. You calculate it with z = (X − μ) / σ, which centers the data at zero and scales by the spread. This standardization lets you compare values from different distributions or scales because all z-scores map onto a common reference—the standard normal distribution with mean 0 and SD 1.

Think of the other statistics as describing different things: the average is the central tendency, the range is the span from lowest to highest value, and the standard deviation is the average distance from the mean (a measure of dispersion). The z-score, in contrast, expresses that distance in units of standard deviation.