If the standard deviation for a set of data is $0$, what does this indicate about the data values?

• A. The mean of the data set is $0$.
• B. All the data values are the same.
• C. The data values are spread out over a wide range.
• D. There is exactly one outlier in the data set.

Answer: (B)

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 zero means there is no variation or spread in the data values.
3. Since standard deviation is calculated based on the squared differences between each data value and the mean, if all these differences are zero, it implies every data value is equal to the mean.
4. Therefore, when the standard deviation is zero, it indicates that all data values in the set are identical.
5. This means the data set has no spread or variability, and the mean is equal to each data value.