Answer :
Final answer:
To find the mean mark for the girls, we calculated the total marks for the class and for the boys, subtracted the boys' total from the class total to get the girls' total, and divided by the number of girls. The mean mark for the girls in class 10R is 76%.
Explanation:
The question asks us to work out the mean mark for the girls in a class where the overall mean mark is known, along with the mean mark for the boys and the distribution of genders in the class. We have 30 students in class 10R with a mean mark of 70% and 10 boys with a mean mark of 58%. We need to find the mean mark for the girls.
Steps to Solve:
Calculate the total marks for all students: Total marks = Mean mark * Number of students = 70% * 30 = 2100%.
Calculate the total marks for the boys: Total marks (boys) = Mean mark (boys) * Number of boys = 58% * 10 = 580%.
Subtract the total marks of the boys from the total marks for all students to find the total marks for the girls: Total marks (girls) = Total marks - Total marks (boys) = 2100% - 580% = 1520%.
Calculate the number of girls: Number of girls = Total number of students - Number of boys = 30 - 10 = 20.
Calculate the mean mark for the girls: Mean mark (girls) = Total marks (girls) / Number of girls = 1520% / 20 = 76%.
The mean mark for the girls in class 10R is 76%.
