A diploma student scored 72 in a paper carrying 4 credits, 60 in a paper carrying 3 credits and 84 in a paper carrying 1 credit. Each paper counts as many times as the credits it carries. What is the student's average score?

Count each score as often as its credits: $72\times 4+60\times 3+84\times 1=288+180+84=552$, spread over 4 + 3 + 1 = 8 credits, so the average is 552/8 = 69. 72 is the plain average of 72, 60 and 84, treating three papers as equally important when one of them carries four times the weight of another. 73.5 pairs the credits with the wrong papers, giving 1 credit to the 72 and 4 to the 84. 184 divides the correct weighted total of 552 by 3, the number of papers, rather than by 8, the number of credits.