Two classes took the same test. One class of 25 students made an average grade of 82%, the other class of 32 students made an average grade of 75%. The average grade for all students in both classes is approximately:
Correct Answer: Option B
The total number of students = 25 + 32 = 57
We know that, Average = (Sum of all terms)/(total no. of terms)
∵ Students from class I scored at an average of 82,
82 = (Sum of scores of students from class I)/25
∴ Sum of scores of students from class I = 82 × 25 = 2050
Similarly,
∵ Students from class II scored at an average of 75,
75 = (Sum of scores of students from class II)/32
∴ Sum of scores of students from class II = 32 × 75 = 2400
∴Average of all 57 students= (Sum of grades of all 57 students)/(total number of students)
⇒ Average \(= \;\frac{{2050{\rm{\;}} + {\rm{\;}}2400}}{{57}} = \frac{{4450}}{{57}}\)
⇒ Average = 78.07 ≈ 78
∴ Average % of all students is approximately 78%
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