A z-score standardizes a raw value by expressing its distance from the mean in standard deviation units. The formula is z = (x − μ)/σ, where x is the observed value, μ is the mean, and σ is the standard deviation. The numerator x − μ measures how far the value is from the mean. Dividing by σ converts that distance into standard deviation units. A positive z-score means the value is above the mean, a negative z-score means the value is below the mean, and z = 0 means the value equals the mean. Option B divides the raw value by the mean and does not measure standardized distance. Option C reverses the ratio incorrectly. Option D gives only the raw deviation and fails to standardize by the standard deviation. Z-scores are central in normal distribution calculations and comparisons across different scales. Study Guide references/topics: z-score, standardization, mean, standard deviation.
