Final answer:
A data set with a standard deviation of 0 indicates no variation; thus, all data values are identical. In this case, all values being 12 is the correct dataset configuration.
Step-by-step explanation:
The question concerns a set of data with ten numbers, a mean of 12, and a standard deviation of 0. When a data set has a standard deviation equal to zero, it implies that all of the data values are identical since there's no variation or spread in the data. Therefore, the correct option for a data set with these statistics is that all values are 12, denoted by option (a). Options (b), (c), and (d) are not correct because they imply variation, which would result in a standard deviation greater than zero.
When the standard deviation is zero, it means that all of the data have the same value. In this case, the mean of the data is 12, so all of the numbers in the data set must be 12 in order for the standard deviation to be zero.