Mean of Grouped Data

1. The mark obtained by 30 students of class 6th in physics paper consisting of 100 marks are given in below table. Find the mean of marks obtained by the students?

Marks   obtained     xi	10	20	36	40	50	56	60	70	72	80	88	92	95
Number   of students       fi	1	1	3	4	3	2	4	4	1	1	2	3	1

Solution: To find the mean marks, we require the   product of each x_i with the corresponding frequency f_i so, let us arrange in below table.

Mark obtained    xi	Number of         students   fi	fixi
10	1	10
20	1	20
36	3	108
40	4	160
50	3	150
56	2	112
60	4	240
70	4	280
72	1	72
80	1	80
88	2	176
92	3	276
95	1	95
Total	𝝨fi = 30	𝝨 fixi =1779

                            Mean = 𝝨 f_ix_i/𝝨x_i                  

= 1779/30                             

 = 59.3   Therefore, the mean marks obtained is 59.3