What is the interpretation of a z-score of 2?

• A. The observation is two standard deviations above the mean.
• B. The observation is two raw units above the mean.
• C. The observation is in the second percentile.
• D. The observation is twice the mean.

Answer: (A)

A z-score tells you how far a value is from the mean, measured in units of the standard deviation. A z-score of 2 means the value lies two standard deviations above the mean. In formula terms, z = (X − μ)/σ, so if z = 2 then X = μ + 2σ. If the distribution is roughly normal, this corresponds to about the 97.7th percentile, meaning it’s higher than about 97.7% of observations. This clarifies why it’s not two raw units above the mean, not twice the mean, and not the second percentile—the interpretation focuses on distance from the mean in standard deviation units.