Multiple choice

Students of three sections of a class, having 30, 30 and 40 students, respectively, appeared for a test of 100 marks. The arithmetic means of the marks of the three sections are 72.2, 69.0 and 64.1 in that order. What is the arithmetic mean of the marks of all the students of three sections?

  1. 66.6

  2. 67.3

  3. 68.0

  4. 70.6
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C Correct answer
Explanation

Weighted mean = (30*72.2 + 30*69.0 + 40*64.1) / (30+30+40) = (2166 + 2070 + 2564) / 100 = 6800 / 100 = 68.0.

AI explanation

Using the combined arithmetic mean formula, the overall mean is calculated by dividing the total marks of all students by the total number of students. The total marks are (30 multiplied by 72.2) plus (30 multiplied by 69.0) plus (40 multiplied by 64.1), which equals 2166 + 2070 + 2564 = 6800. The total number of students is 30 + 30 + 40 = 100. Dividing 6800 by 100 gives an overall arithmetic mean of 68.0.

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