The article introduces the notion of a non-associativity degree for a triple of elements of a commutative idempotent groupoid and the notion of the groupoid non-associativity degree. For groupoids with a finite non-associativity degree, a symmetric idempotent ternary operation was constructed as a continuation of a binary operation. In this paper, the groupoid of ordered partitions of a finite set with an aggregated sum subjected to systematic investigation for the first time. Some general results on the degree of non-associativity are obtained and the results of numerical analysis are presented.