totalsummor

Totalsummor is a theoretical operator used in mathematics and data analysis to generate a single scalar summary from a collection of numeric totals. It generalizes simple summation by allowing a weighted combination of sub-totals, enabling flexible aggregation across sources or groups. The term is a portmanteau of total and summation, and while not widely standardized, it appears in contemporary discussions of data aggregation.

Let A1, A2, ..., Am be finite multisets of real numbers, with sub-totals s_i = sum_{x in A_i} x. Given a weight vector w = (w1,...,wm) with w_i ≥ 0 and sum w_i = 1, the totalsummor of the collection is T = sum_{i=1}^m w_i s_i. If all weights are equal, T equals the average of the sub-totals; if a single weight is 1, T equals that sub-total.

Variants may apply to matrices by taking the sums of columns or rows, followed by a second-stage weighted combination. For example, A1={2,3}, s1=5; A2={1,4,-1}, s2=4. With equal weights, T = (5+4)/2 = 4.5. With weights 0.3 and 0.7, T = 0.3*5 + 0.7*4 = 4.3.

Totalsummor is used as a compact summary when sources vary in importance or size, such as budgeting from multiple departments or combining experimental results. Its value depends on the chosen weights, and critics note that the interpretation of totalsummor can change with different weightings, potentially obscuring raw totals.

See also: sum, weighted sum, aggregation, normalization.