Question

A class consists of 50 students out of which 30 are girls. The mean of marks scored by girls in a test is 73 (out of 100) and that of boys is 71. Determine the mean score of the whole class.

Answer 1

Hint: Here we have to calculate the mean score of the whole class. We will first calculate the total marks scored by girls by multiplying the number of girls with the mean marks scored by girls. Then we will calculate the total marks scored by the boys by multiplying the number of boys with the mean marks scored by the boys. We will then calculate the total marks scored by all students by adding the marks scored by boys and girls. To calculate the mean score of the whole class, we will divide the total marks scored by students by the total number of students.

Complete step-by-step answer:
It is given that:-
Total number of students \[ = 50\]
Number of girls \[ = 30\]
Therefore, number of boys \[ = 50 - 30 = 20\]
Mean marks scored by girls \[ = 73\]
We will calculate the total marks scored by the girls.
Total marks scored by girls \[ \div \] number of girls \[ = \] mean marks scored by girls
Substituting the value of mean marks scored by girls and number of girls, we get
\[ \Rightarrow \] Total marks scored by girls \[ \div 30 = 73\]
Simplifying the terms, we get
\[ \Rightarrow \] Total marks scored by girls \[ = 73 \times 30 = 2190\]………….\[\left( 1 \right)\]
We will calculate the total marks scored by the boys.
\[ \Rightarrow \] Total marks scored by boys \[ \div \] number of boys \[ = \] mean marks scored by boys
Substituting the value of mean marks scored by boys and number of boys, we get
\[ \Rightarrow \] Total marks scored by boys \[ \div 20 = 71\]
Simplifying the terms, we get
\[ \Rightarrow \] Total marks scored by boys \[ = 71 \times 20 = 1420\]………….\[\left( 2 \right)\]
Thus, the marks scored by the whole class are equal to the sum of total marks scored by girls and the total marks scored by boys.
Therefore,
Total marks scored by whole class \[ = 2190 + 1420 = 3610\]
Now, we will calculate the mean marks scored by the whole class.
Mean marks scored by class \[ = \] total marks scored by whole class \[ \div \] number of students
Substituting the total marks scored by whole class and number of students in the above equation, we get
\[ \Rightarrow \] Mean marks scored by class \[ = \dfrac{{3610}}{{50}} = 72.2\]
Hence, the mean score of the class is 72.2.

Note: Mean is also known as an average and it is the ratio of sum of all the numbers to the number of numbers. If we increase the sum of the numbers by adding more numbers then arithmetic mean also increases.