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

• A. The $standarddeviation$ is affected by outliers.
• B. The $standarddeviation$ is measured in the same units as the data.
• C. The $standarddeviation$ can be larger than the $range$ of the data.
• D. The $standarddeviation$ is always non-negative.

Answer: (C)

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 affected by outliers because it depends on the squared deviations from the mean, which gives more weight to extreme values.
3. Step 3: Remember 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. Step 4: Note that the standard deviation is always non-negative because it is derived from squared differences, which cannot be negative, and then taking a square root.
5. Step 5: Evaluate the statement about the standard deviation being larger than the range. Since the range is the difference between the maximum and minimum values, the standard deviation cannot exceed this range, making this statement false and thus not a property of the standard deviation.