In a school 40 percent of the students pay a monthly fee of ₹1,200, another 35 percent pay ₹900 and the rest pay ₹600. What is the mean fee per student, in ₹?

The three groups are of different sizes, so each fee must be weighted by its share of the students. The last group is 100 − 40 − 35 = 25 percent, and the mean fee is 0.40(1200) + 0.35(900) + 0.25(600) = 480 + 315 + 150 = ₹945. Averaging the three fees as (1200 + 900 + 600)/3 = ₹900 treats the groups as equally large. Attaching the weights to the wrong fees, 0.25(1200) + 0.35(900) + 0.40(600), gives ₹855, and ₹1,050 is just the average of the two largest fees.