Final answer:
The range of a dataset consisting of isolated values is described as having a discrete distribution, similar to a line spectrum in physics. This type of distribution can have a standard deviation of zero if there is no variability, indicating that all data points are identical.
Step-by-step explanation:
When the range of a dataset consists exclusively of one or more isolated values, it is typically described as having a discrete distribution. In contrast to a continuous spectrum where you have an unbroken range of values, a dataset with a discrete distribution will have specific, individual points. A line spectrum in physics, for example, consists of specific wavelengths where light is emitted or absorbed, which is analogous to the discrete data points we see in statistics.
A standard deviation (standard deviation) of zero for this type of distribution would indicate no variability within the data, as all values are identical. However, when the standard deviation is larger than zero, we see more variability and spread around the mean. For conceptual understanding, consider the domain of a random variable in probability, which could be a discrete set such as types of hair color, where each outcome is distinct and non-continuous.