 Hello and welcome to the session. In this session we are going to discuss the following question which says that in a class of 50 students the average marks of 20 girls is 40 and that of 30 boys is 42, find the new marks of the entire class. In this question we are given that there are 50 students in a class out of which 20 are girls and 30 are boys. Also the average marks of 20 girls is given as 40 and that of 30 boys is given as 42, you have to find the new marks of the entire class. We know that when two sets of scores have been combined into a single distribution then the name of the combined distribution is the weighted mean of the, of the components. Therefore, mean of the combined distribution denoted by x bar is equal to m1 x1 bar plus m2 x2 bar whole divided by m1 plus m2 where x bar is the mean of the combined distribution x1 bar and x2 bar are the mean of the component distribution m1 and m2 is the total frequency of the component distribution. So we say that the mean of the combined distribution is given by the formula x bar equal to m1 x1 bar plus m2 x2 bar whole divided by m1 plus m2 where x1 bar and x2 bar are the mean of the component distribution and m1 and m2 is the total frequency of the component distribution. This is the key idea we shall be using in this question. Now moving on to the solution, it is given in the question that out of 50 students the average marks of 20 girls is 40 and the average marks of 30 boys is 42 and we have to find out the mean marks of the entire class. Let us assume that the mean marks of the entire class be x bar also let x1 bar and x2 bar denote the average marks of girls and boys respectively. Then from the question it is clear that the value of x1 bar that is the average marks for 20 girls is 40 and the value of x2 bar that is the average marks for 30 girls is 42 also we have m1 is equal to 20 and m2 equal to 30. Then we can write x1 bar equal to 30 the value of x2 bar is equal to 32 m1 is 20 and m2 is 30. We have to find the mean marks of the entire class given by x bar here we use the key idea which states that when two sets of scores have been combined into a single distribution then the mean of the combined distribution is the weighted mean of the mean of the components which is given by the formula x bar is equal to m1 x1 bar plus m2 x2 bar whole divided by m1 plus m2 if the value of m1 m2 x1 bar x2 bar are known then we can easily find the value of the combined mean. Therefore, average marks of the entire class is given by x bar equal to m1 x1 bar plus m2 x2 bar whole divided by m1 plus m2. On putting the required values in the equation we get the value of x bar as 20 multiplied by 40 plus 30 multiplied by 42 whole divided by 20 plus 30. Or we can write x bar as 800 plus 1260 divided by 50. Or x bar is equal to 2060 divided by 50 which gives the value of x bar as 31 decimal 2. Therefore, the average marks of the entire class 41 decimal 2 which is the required answer. This completes the session. Hope you have understood it well.