What does the 'mean' refer to in a Poisson distribution?

In a Poisson distribution, the 'mean' specifically refers to the average number of occurrences of an event within a given interval of time or space. This parameter, often denoted by the symbol λ (lambda), quantifies the central tendency of the distribution, reflecting how often an event is expected to happen over the defined interval.

In practical terms, if you were modeling something like the number of phone calls received at a call center in an hour using a Poisson distribution, the mean would tell you the expected number of calls in that time frame. Each occurrence is independent of the others, and the mean serves as a critical point of reference for understanding the distribution's behavior and predicting future occurrences.

Other choices do not accurately represent the concept of the mean in the context of a Poisson distribution. The maximum frequency discusses a different concept, while total possible outcomes and standard deviation relate to the distribution's overall structure and variability rather than its average occurrence rate. Thus, the definition of the mean as the average number of occurrences in a specified interval is the correct interpretation within the context of a Poisson distribution.