 Hello and welcome to the session. In this session we are going to discuss the following question which says that a student obtained 70 marks in English, 60 marks in Hindi, 90 marks in mathematics, 50 marks in science and 35 marks in social studies calculate the weighted mean of the marks if weights are 2, 2, 5, 5 and 3 respectively. Weighted mean denoted by x w bar is given by x w bar is equal to w 1 x 1 plus w 2 x 2 and so on plus w n x n upon w 1 plus w 2 and so on up to w n which can also be written as x w bar is equal to summation of i is running from 1 to n w i into x i whole upon summation of i is running from 1 to n w i or simply we can write x w bar is equal to summation w x upon summation w. With this key idea we shall proceed with the solution. Here the marks of a student in 5 subjects is given as 70 in English, 60 in Hindi, 90 in mathematics, 50 in science and 45 in social studies. We need to calculate the weighted mean of the marks if the weights are given by 2, 2, 5, 5 and 3 respectively. Let x i be the marks of the student and w i be the corresponding weight then the value of x 1 is given by 70, x 2 is 60, x 3 is equal to 90, x 4 is equal to 50 and x 5 is equal to 45. Also w 1 is given by 2, w 2 is equal to 2, w 3 is equal to 5, w 4 is equal to 5 and w 5 is equal to 3. We know that weighted mean denoted by x w bar is given by summation w i x i where i is running from 1 to n upon summation w i where i is running from 1 to n. Therefore weighted mean of the marks is given by summation w i x i where i goes from 1 to 5 upon summation w i where i goes from 1 to 5 which is equal to summation w i x i where i goes from 1 to 5 can be written as w 1 x 1 plus w 2 x 2 plus w 3 x 3 plus w 4 x 4 plus w 5 x 5 upon summation w i where i goes from 1 to 5 can be written as w 1 plus w 2 plus w 3 plus w 4 plus w 5. Now we have the values of x 1, x 2, x 3, x 4, x 5 also w 1, w 2, w 3, w 4 and w 5. Substituting all these values we get w 1 x 1 that is 2 into 70 plus w 2 x 2 that is 2 into 60 plus w 3 x 3 that is 5 into 90 plus w 4 x 4 that is 5 into 50 plus w 5 x 5 that is 3 into 135 whole upon w 1 that is 2 plus w 2 that is 2 plus w 3 5 plus w 4 5 plus w 5 that is 3. Therefore we get 140 plus 120 plus 450 plus 250 plus 135 whole upon 17 which is equal to 1095 by 17 that is 64.41 so x w bar is given by 64.41 therefore the weighted mean of the marks is given by 64.41 which is the required answer this completes our session hope you enjoyed this session