The subject is quite ambiguous. Let me use an example to clarify.
For example, we have a patient booking schedule for a doctor, which specifies the schedule time for patients. There are so many randomness to affect how this day goes, such as patient arriving early/late, unexpected long visits, etc. Our goal is to predict the final ending time (the leave time for last patient).
Let's say we designed a simulation tool by considering all those randomness and we run this tool 100 iterations. In this way, we get a 100x1 vector a = [a1, a2, a3,..., a100], each of which is the returning ending time result for that simulation iteration.
The question is: what is our predict for ending time? I first though we should take the mean or median for this vector. Then I realized most likely I am wrong since a result for example [16, 16, 16, 17] will get a mean of 16.25 and I think in this case 16 should be the answer. Perhaps the answer is just the result occurs most in these 100 iterations, but how to mathematically formulate this? Thanks.