Final answer:
When the standard deviation of a data set is equal to zero, it means that all of the data values have the same value and there is no variation or spread in the data set.
Step-by-step explanation:
When a data set has a standard deviation equal to zero, it means that all of the data values have the same value. In other words, there is no variation or spread in the data set. This can happen when all the measurements were taken with the same method or instrument, or when the data set only consists of one unique value.