Which of the following is not a property of the $standarddeviation$?

• A. The $standarddeviation$ is zero if all data values are identical.
• B. The $standarddeviation$ is affected by extreme values ($outliers$).
• C. The $standarddeviation$ is always $\ge 0$.
• D. The $standarddeviation$ is equal to the $mean$ of the data.

Answer: (D)

Verified step by step guidance

1. Recall the definition of standard deviation: it measures the average amount by which data values deviate from the mean of the dataset.
2. Understand that the standard deviation is zero if all data values are identical because there is no variability; every value equals the mean.
3. Recognize that the standard deviation is sensitive to extreme values (outliers) because these values increase the average squared deviation from the mean.
4. Note that the standard deviation is always non-negative since it is derived from squared deviations, which cannot be negative, and then taking a square root.
5. Identify that the statement 'The standard deviation is equal to the mean of the data' is incorrect because the standard deviation and the mean measure different aspects: the mean measures central tendency, while the standard deviation measures spread.