What is the effect of increasing the mean while keeping SD constant on the Z-score for a fixed observed result?

What is the effect of increasing the mean while keeping SD constant on the Z-score for a fixed observed result?

• A. Z-score increases.
• B. Z-score decreases.
• C. Z-score remains the same.
• D. Z-score becomes undefined.

Answer: (B)

Z-score is the standardized distance from the mean: z = (observed value − mean) / SD. If you hold the observed value and the standard deviation constant and increase the mean, the difference (observed − mean) gets smaller. Since the denominator (SD) doesn’t change, the overall z-value moves closer to zero and becomes smaller in value. If the mean passes the observed value, the Z-score becomes negative, with zero occurring when the mean equals the observed value. Thus, increasing the mean with constant SD lowers the Z-score.

Z-score is the standardized distance from the mean: z = (observed value − mean) / SD. If you hold the observed value and the standard deviation constant and increase the mean, the difference (observed − mean) gets smaller. Since the denominator (SD) doesn’t change, the overall z-value moves closer to zero and becomes smaller in value. If the mean passes the observed value, the Z-score becomes negative, with zero occurring when the mean equals the observed value. Thus, increasing the mean with constant SD lowers the Z-score.