If 12 numbers have an average of 35, and each number is first reduced by 4 and the result then halved, what is the average of the 12 new numbers?

The same two steps applied to every number are applied to the average as well, and in the same order: (35 - 4)/2 = 31/2 = 15.5. The count 12 never enters the working. 13.5 halves first and subtracts afterwards (35/2 - 4), reversing the order - these two steps do not commute. 31 stops after the subtraction and 17.5 stops after the halving; each carries out only one of the two instructions.