If a sample has a standard deviation of $0$, what does this indicate about the data values in the sample?

• A. All data values in the sample are identical.
• B. The sample has a normal distribution.
• C. There is a calculation error in the data.
• D. The mean of the sample is $0$.

Answer: (A)

Verified step by step guidance

1. Recall the definition of standard deviation: it measures the amount of variation or dispersion of a set of data values from their mean.
2. Understand that a standard deviation of 0 means there is no variation in the data values; all values are exactly the same as the mean.
3. Recognize that if all data values are identical, the difference between each data point and the mean is zero, which leads to a standard deviation of zero.
4. Note that a standard deviation of zero does not imply anything about the distribution shape (such as being normal) or the mean value itself.
5. Conclude that the correct interpretation is that all data values in the sample are identical.