What is the formula for a z-score?

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

Answer: (A)

A z-score shows how many standard deviations a value is from the mean, which allows you to compare scores from different distributions on a common scale. Start by centering the value around the mean so the mean becomes zero, then rescale by dividing by the standard deviation so one unit in the z-score equals one standard deviation of the data. This makes the result dimensionless and enables direct comparison across datasets.

So the z-score is computed as z = (x − μ) / σ. If x equals the mean, z is 0; if x is one standard deviation above the mean, z is 1; if it’s two standard deviations below, z is −2, and so on.

Note that with sample data you might see z-scores written using the sample mean and sample standard deviation, (x − x̄)/s, but the core idea remains the same: subtract the mean to center, then divide by the standard deviation to standardize.