Which statement is true about a z-score of 0.5?

• A. The observation is below the mean
• B. The observation is two standard deviations above the mean
• C. The observation is half a standard deviation above the mean
• D. The observation is exactly at the mean

Answer: (C)

A z-score shows how far and in which direction a value lies from the mean, measured in units of standard deviation. A z-score of 0.5 means the observation is 0.5 standard deviations above the mean. This comes directly from the definition z = (X − μ) / σ, so X = μ + 0.5σ. It indicates the value is to the right of the mean, but not far above it—only halfway to one standard deviation above the mean. It is not below the mean, not two standard deviations above, and not exactly at the mean.