Question

Class 10R sat a test

The mean mark for the class was 70%.
There are 30 students in class 10R, 20 of whom are boys.
The mean mark for the boys is 62%.
Work out the percentage for the girls

Answer 1

86%

Explanation:

You want the girls' average if the 20 boys in the 30-student class had an average of 62%, and the class average was 70%.

Weighted average

The class average is the weighted average of the boys' score and the girls' score. The weights are the fraction of students of each gender.

class average = (1/3)(girls' average) +(2/3)(boys' average)

Girls' average

Solving this equation for the girls' average, we get ...

(1/3)(girls' average) = (class average) -(2/3)(boys' average)

girls' average = 3(class average) -2(boys' average)

girls' average = 3(70%) -2(62%) = 210% -124%

girls' average = 86%

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Alternate solution

The sum of differences from the class average must be zero. The boys' average is 8 points below the class average, and there are 2 times as many boys as girls. Thus, compared to the girls, the boys contribute a total of 2·8 = 16 points below the class average. The girls must counter by having an average 16 points above the class average: 70+16 = 86.