Which of the following is not a property of the $s$tandard deviation?

• A. The $s$tandard deviation is affected by outliers.
• B. The $s$tandard deviation is always $\ge 0$.
• C. The $s$tandard deviation is always less than the $mean$.
• D. The $s$tandard deviation is measured in the same units as the data.

Answer: (C)

Verified step by step guidance

1. Recall the definition of standard deviation: it measures the average amount by which data points deviate from the mean of the dataset.
2. Understand that the standard deviation is always non-negative because it is derived from squared deviations, which cannot be negative, and then taking a square root.
3. Recognize that the standard deviation is measured in the same units as the original data since it is the square root of the variance (which is in squared units).
4. Know that the standard deviation is sensitive to outliers because extreme values increase the average deviation from the mean.
5. Evaluate the statement 'The standard deviation is always less than the mean' and realize this is not necessarily true, as the standard deviation can be greater than, less than, or equal to the mean depending on the data distribution.