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Answer :
Final answer:
To calculate the mean mark for the girls in class 10R, subtract the total sum of the boys' marks from the total sum of the class's marks, then divide by the number of girls, resulting in a mean mark of 86% for the girls.
Explanation:
To find the mean mark for the girls in class 10R, we need to first understand that the mean mark for the entire class is the sum of all the students' marks divided by the number of students. Given that the mean mark is 70% and there are 30 students in the class, we can calculate the total sum of marks for the class (which is the mean multiplied by the number of students).
Total sum of marks for the class = mean imes number of students = 70% imes 30 = 2100%
Next, we calculate the total sum of marks for the boys, knowing that their mean mark is 62% and there are 20 boys.
Total sum of marks for the boys = mean of the boys imes number of boys = 62% imes 20 = 1240%
Subtracting the total sum of the boys' marks from the total sum of the class's marks gives us the total sum of the girls' marks.
Total sum of marks for the girls = total sum for the class - total sum for the boys = 2100% - 1240% = 860%
Since the number of girls in the class is the total number of students minus the number of boys (30 - 20), there are 10 girls in the class. Finally, we can find the mean mark for the girls by dividing the total sum of their marks by the number of girls.
Mean mark for the girls = Total sum of marks for the girls \/ number of girls = 860% \/ 10 = 86%
Therefore, the mean mark for the girls in class 10R is 86%.
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