On mean type aggregation

We introduce and define the concept of mean aggregation of a collection of n numbers. We pointout that the lack of associativity of this operation compounds the problem of the extending mean of n numbers to n + 1 numbers, The closely related concepts of self identity and the centering property are introduced as one imperative for extending mean aggregation operators, The problem of weighted mean aggregation is studied, A new concept of prioritized mean aggregation is then introduced. We next show that the technique of selecting an element based upon the performance of a random experiment can considered as a mean aggregation operation.