Answer: Scores below and above the mean in units of the standard deviation of the distribution from the mean

## 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.

Author: Nikitesh Somanthe