If the control result equals the control mean, the Z-score is

If the control result equals the control mean, the Z-score is

• A. 0
• B. 1
• C. -1
• D. Undefined

Answer: (A)

The Z-score measures how far a value is from the mean in units of the standard deviation: Z = (X − μ) / σ. If the control result equals the control mean, then X = μ, so Z = (μ − μ) / σ = 0, provided the standard deviation σ is not zero. In standard practice, there is some variation, so σ > 0, making the Z-score zero. A Z-score of +1 or −1 would mean the result is one standard deviation above or below the mean, not equal to it. An undefined Z-score would occur only if there is no variation in the control data (σ = 0), which is not a typical or valid scenario for calculating a Z-score.

The Z-score measures how far a value is from the mean in units of the standard deviation: Z = (X − μ) / σ. If the control result equals the control mean, then X = μ, so Z = (μ − μ) / σ = 0, provided the standard deviation σ is not zero. In standard practice, there is some variation, so σ > 0, making the Z-score zero.

A Z-score of +1 or −1 would mean the result is one standard deviation above or below the mean, not equal to it. An undefined Z-score would occur only if there is no variation in the control data (σ = 0), which is not a typical or valid scenario for calculating a Z-score.