What is the z-score normalization (standardization) of a data point x in a dataset with mean μ and standard deviation σ?

• A. z = (μ − x) / σ
• B. z = (x − μ) / σ
• C. z = (x − μ) * σ
• D. z = (x + μ) / σ

Answer: (B)

Standardization expresses where a value lies relative to the dataset’s mean in units of the standard deviation. To do this, you subtract the mean and then divide by the standard deviation. That gives the z-score: z = (x − μ) / σ.

Subtracting the mean centers the data at zero, and dividing by the standard deviation scales it so one unit in z corresponds to one standard deviation from the mean. This makes different datasets comparable and yields a dimensionless value.

If you used μ − x, you’d get the opposite sign, which is not the standardization. Multiplying by σ would scale but not center or standardize to unit variance. Adding the mean would shift the data but not normalize its spread.