Which of the following statements is true of the $standarddeviation$?

• A. The $standarddeviation$ is unaffected by outliers.
• B. The $standarddeviation$ is always larger than the $mean$.
• C. The $standarddeviation$ can be negative.
• D. The $standarddeviation$ measures the average distance of data points from the $mean$.

Answer: (D)

Verified step by step guidance

1. Recall the definition of standard deviation: it is a measure of the spread or dispersion of a set of data points around the mean.
2. Understand that the standard deviation is calculated as the square root of the variance, where variance is the average of the squared differences between each data point and the mean.
3. Recognize that because it is based on squared differences, the standard deviation is always a non-negative value; it cannot be negative.
4. Note that the standard deviation is sensitive to outliers because outliers increase the squared differences, thus increasing the variance and standard deviation.
5. Conclude that the standard deviation represents the average distance of data points from the mean, making the statement 'The standard deviation measures the average distance of data points from the mean' true.