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A class of 30 students appeared in a test. The average score of 12 students is 80, and that of the rest is 75. What is the average score of the class?
56
87
67
77
77
Use weighted average formula: Average = (n1A1 + n2A2) / (n1 + n2), where n1 = 12, A1 = 80, n2 = 18, A2 = 75.
Total students in the class = 30, Average score of 12 students = 80, Average score of the remaining students = 75
Average=Total Number of StudentsTotal Sum of Scores
Use weighted average formula: Average = (n1A1 + n2A2) / (n1 + n2), where n1 = 12, A1 = 80, n2 = 18, A2 = 75.
Students often forget to calculate the number of remaining students as 30 - 12 = 18, and instead use 12 or 30 for both groups.
Calculate the total score of the first 12 students
Multiply the number of students (12) by their average score (80).
Sum1=12×80=960
Find the number and total score of the remaining students
Remaining students = 30−12=18. Multiply this by their average score (75).
Sum2=18×75=1350
Calculate the total sum of scores for all 30 students
Add the sum of scores from both groups.
Total Sum=960+1350=2310
Find the average score of the entire class
Divide the total sum of scores by the total number of students (30).
Average=302310=77
D is correct because the average score of the class calculated as total sum of scores divided by total students equals 77.
Average problems frequently appear in data interpretation and mixture-alligation topics.
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