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

• A. The $standarddeviation$ is always $\ge 0$.
• B. The $standarddeviation$ is affected by extreme values (outliers).
• C. If all values in a data set are the same, the $standarddeviation$ is $0$.
• D. The $standarddeviation$ is equal to the $mean$ of the data.

Answer: (D)

Verified step by step guidance

1. Step 1: Understand what the standard deviation measures. It quantifies the amount of variation or dispersion in a set of data values.
2. Step 2: Recall that the standard deviation is always non-negative because it is derived from squared differences, which cannot be negative.
3. Step 3: Recognize that the standard deviation is sensitive to extreme values (outliers) because these values increase the squared differences from the mean, thus increasing the standard deviation.
4. Step 4: Note that if all values in a data set are identical, there is no variation, so the standard deviation is zero.
5. Step 5: Identify that the statement 'The standard deviation is equal to the mean of the data' is not a property of the standard deviation, as the mean and standard deviation measure different aspects of the data.