Yes, it is indeed possible for a data set to have no mode. The mode of a data set is defined as the value that appears most frequently. If no number in the data set repeats, then there will be no mode.
For example, consider the data set: {1, 2, 3, 4, 5}. In this case, each number appears exactly once, meaning none of them is repeated. Since there is no number that occurs more frequently than the others, we can conclude that this data set has no mode.
Additionally, it’s also possible for a data set to have more than one mode, which is known as a multimodal set. Conversely, when a data set has two modes, it is referred to as bimodal.