Explanation

Correct Answer: D

Why D is correct:

1. Z-score formula: z = (X - μ)/σ

   • X = raw score
   • μ = population mean
   • σ = population standard deviation

2. Interpretation:

   • The z-score measures how many standard deviations a data point is from the mean
   • It indicates both direction (positive = above mean, negative = below mean) and magnitude (number of standard deviations)
   • Option D accurately captures that z-scores represent scores both below AND above the mean in units of standard deviation FROM the mean

Why other options are incorrect:

• A: Missing "from the mean" - z-scores specifically measure distance from the mean, not just in standard deviation units
• B: Incorrectly mentions "variance" instead of "mean" - z-scores are based on the mean, not variance
• C: Only mentions "above the mean" - z-scores represent both above AND below the mean

Key Concept: A z-score (standard score) is a statistical measurement that describes a value's relationship to the mean of a group of values. It is measured in terms of standard deviations from the mean. If a z-score is 0, it indicates that the data point's score is identical to the mean score. A z-score of 1.0 indicates a value that is one standard deviation from the mean. Z-scores may be positive or negative, with a positive value indicating the score is above the mean and a negative score indicating it is below the mean.