What does a Z-score represent?

What does a Z-score represent?

• A. The absolute difference between the control result and the expected mean.
• B. The ratio of the control result to the mean.
• C. The number of standard deviations a value is from the mean.
• D. The probability that the control result occurs.

Answer: (C)

A Z-score shows how many standard deviations a value is from the mean. It’s found by subtracting the mean from the value and dividing by the standard deviation, which standardizes the result so you can compare measurements across different tests or datasets. For example, with a mean of 100 and a standard deviation of 15, a value of 115 has a Z-score of +1 (one standard deviation above the mean), while a value of 70 has a Z-score of −2 (two standard deviations below). This concept matters in QC because it lets you judge whether a result is typical or unusual relative to the expected variation. The other descriptions don’t fit because: an absolute difference ignores variability and is in original units; a ratio to the mean is not standardized by dispersion; and the Z-score itself is not a probability, though it can be used with the standard normal distribution to estimate how likely certain values are.

A Z-score shows how many standard deviations a value is from the mean. It’s found by subtracting the mean from the value and dividing by the standard deviation, which standardizes the result so you can compare measurements across different tests or datasets. For example, with a mean of 100 and a standard deviation of 15, a value of 115 has a Z-score of +1 (one standard deviation above the mean), while a value of 70 has a Z-score of −2 (two standard deviations below). This concept matters in QC because it lets you judge whether a result is typical or unusual relative to the expected variation.

The other descriptions don’t fit because: an absolute difference ignores variability and is in original units; a ratio to the mean is not standardized by dispersion; and the Z-score itself is not a probability, though it can be used with the standard normal distribution to estimate how likely certain values are.