sentences:  The data used are prices and quantities in two time-periods, (t-1) and (t), for each of "n" goods which are indexed by "i".If we denote the price of item "i" at time t-1 by formula_1, and, analogously, we define formula_2 to be the quantity purchased of item "i" at time t, then, the Törnqvist price index formula_3 at time t can be calculated as follows