The average score of students on a test in Section A is 72 and that of students in Section B is 76. What is the combined average of both the sections given that Section A has 30 students and Section B has 25 students?
Step-by-step solution
To find: The combined average score of all 55 students
Idea: Turn each average back into a total (average × number of students), add the totals, and divide by the total number of students.
- Total score of Section A = 72 × 30 = 2160; total score of Section B = 76 × 25 = 1900.½ mark
- Total of both sections = 2160 + 1900 = 4060; number of students = 30 + 25 = 55.½ mark
- Combined average = 406055 = 73.818… ≈ 73.82.1 mark
Check: 73.82 is between 72 and 76, and a little closer to 72 because Section A is larger ✓. (Simply averaging gives 74, which is wrong here.)
Answer to write in the exam
Total score of Section A = 72 × 30 = 2160
Total score of Section B = 76 × 25 = 1900
Combined average = 2160 + 190030 + 25 = 406055 = 73.82
∴ Combined average ≈ 73.82
Common mistakes that cost marks
- Giving 72 + 762 = 74. The sections have different sizes, so their averages cannot be weighted equally.
- Multiplying the averages by the wrong section sizes (72 × 25 and 76 × 30).
- Dividing the total by 2 instead of by 55 students.
How this can come in the exam
Section X has 40 students with an average of 65 and Section Y has 10 students with an average of 80. The combined average is
- 72.5
- 68
- 70
- 66
Show answer
(B) 68
40 × 65 + 10 × 8050 = 2600 + 80050 = 340050 = 68.
Try one yourself
Class A has 24 students with an average mark of 58 and Class B has 36 students with an average of 63. Find the combined average.
Show answer
24 × 58 + 36 × 6360 = 1392 + 226860 = 366060 = 61.
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