Which statement about Z-score is true?

Which statement about Z-score is true?

• A. Z-score equals zero when the observed value equals the mean.
• B. Z-score is the same as the mean.
• C. Z-score is the standard deviation.
• D. Z-score is the sum of mean and standard deviation.

Answer: (A)

Z-scores measure how many standard deviations an observation is from the mean, using z = (X − μ) / σ. If the observed value equals the mean, the difference X − μ is zero, so the Z-score is zero. That zero value reflects that the point is exactly at the center of the distribution, not above or below it, and it’s expressed in units of standard deviation to allow comparisons across different datasets. The Z-score is not the mean, not the standard deviation, and not a sum of mean and standard deviation.

Z-scores measure how many standard deviations an observation is from the mean, using z = (X − μ) / σ. If the observed value equals the mean, the difference X − μ is zero, so the Z-score is zero. That zero value reflects that the point is exactly at the center of the distribution, not above or below it, and it’s expressed in units of standard deviation to allow comparisons across different datasets. The Z-score is not the mean, not the standard deviation, and not a sum of mean and standard deviation.