If a z-score is -1.5, what does that indicate?

If a z-score is -1.5, what does that indicate?

• A. The observation is 1.5 standard deviations above the mean.
• B. The observation is 1.5 standard deviations below the mean.
• C. The observation is 1.5 raw units below the mean.
• D. The observation equals the mean.

Answer: (B)

Z-scores show how far a value is from the mean in units of the standard deviation, with the sign indicating direction. A z-score of -1.5 means the observation lies 1.5 standard deviations below the mean. In raw terms, the value would be X = μ + (-1.5)σ = μ − 1.5σ, so it’s below the mean by 1.5 standard deviations. It’s not equal to the mean (that would be a z-score of zero) and not above the mean (the negative sign shows below). In a standard normal distribution, this corresponds to about 6.7% of values falling below that point.

Z-scores show how far a value is from the mean in units of the standard deviation, with the sign indicating direction. A z-score of -1.5 means the observation lies 1.5 standard deviations below the mean. In raw terms, the value would be X = μ + (-1.5)σ = μ − 1.5σ, so it’s below the mean by 1.5 standard deviations. It’s not equal to the mean (that would be a z-score of zero) and not above the mean (the negative sign shows below). In a standard normal distribution, this corresponds to about 6.7% of values falling below that point.