If a value is one standard deviation above the mean, what is its z-score?

If a value is one standard deviation above the mean, what is its z-score?

• A. 1
• B. 0
• C. −1
• D. 2

Answer: (A)

Z-scores show how far a value is from the mean in units of standard deviation. The formula is z = (X − μ) / σ. If a value is one standard deviation above the mean, X = μ + σ, so z = (μ + σ − μ) / σ = 1. This means the value sits one standard deviation above the mean on the standard normal scale. For reference, a value at the mean has z = 0, one standard deviation below has z = −1, and two standard deviations above has z = 2.

Z-scores show how far a value is from the mean in units of standard deviation. The formula is z = (X − μ) / σ. If a value is one standard deviation above the mean, X = μ + σ, so z = (μ + σ − μ) / σ = 1. This means the value sits one standard deviation above the mean on the standard normal scale. For reference, a value at the mean has z = 0, one standard deviation below has z = −1, and two standard deviations above has z = 2.