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There are two sections A and B of a class, consisting of 36 and 44 students, respectively. If the average weight of students of section A is 40 kg and that of section B is 35 kg, find the average weight of the whole class.
36.75 kg
37.75 kg
36.25 kg
37.25 kg
37.25 kg
Use the weighted average formula: Total Average = (36 × 40 + 44 × 35) / (36 + 44). Simplify as: (36 × 40 + 44 × 35) / 80 = (9 × 40 + 11 × 35) / 20 = (360 + 385) / 20 = 745 / 20 = 37.25.
Section A has 36 students with an average weight of 40 kg. Section B has 44 students with an average weight of 35 kg.
Average=Total Students∑Weights=n1+n2(n1×A1)+(n2×A2)
Use the weighted average formula: Total Average = (36 × 40 + 44 × 35) / (36 + 44). Simplify as: (36 × 40 + 44 × 35) / 80 = (9 × 40 + 11 × 35) / 20 = (360 + 385) / 20 = 745 / 20 = 37.25.
Students often wrongly calculate the simple average of the two averages, i.e., (40 + 35) / 2 = 37.5, which ignores the different number of students in each section.
Calculate total weight of Section A
The total weight for Section A is the product of the number of students and their average weight: 36×40.
36×40=1440 kg
Calculate total weight of Section B
The total weight for Section B is the product of the number of students and their average weight: 44×35.
44×35=1540 kg
Calculate total weight and total students
Add the weights and the student counts of both sections to get the overall values.
Total Weight=1440+1540=2980 kg, Total Students=36+44=80
Calculate the average of the whole class
Divide the total weight by the total number of students to find the class average.
Average=802980=37.25 kg
D is correct because the weighted average of the class is 37.25 kg calculated from the sum of total weights divided by the total count of students.
Weighted averages are frequently used in mixture and alligation problems; always remember to use the total quantity as the denominator rather than just the number of groups.
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