Prepare the cumulative frequency table. Marks Number of students 0 - 20 5 20 - 40 11 40 - 60 19 60 - 80 11 80 - 100 4

We are asked to prepare the cumulative frequency table for the given data. Marks Number of students 0 - 20 5 20 - 40 11 40 - 60 19 60 - 80 11 80 - 100 4 Cumulative frequency is the sum of all previous frequencies up to the current point. Cumulative frequency of number of students for marks 0 - 20 = 5 Cumulative frequency of marks of students for marks 20 - 40 = 5 + 11 = 16 Cumulative frequency of marks of students for marks 40 - 60 = 5 + 11 + 19 = 35 Cumulative frequency of marks of students for marks 60 - 80 = 5 + 11 + 19 + 11 = 46 Cumulative frequency of marks of students for marks 80 - 100 = 5 + 11 + 19 + 11 + 4 = 50 So, the cumulative frequency table can be drawn as follows. Marks Number of students Cumulative frequency 0 - 20 5 5 20 - 40 11 16 40 - 60 19 35 60 - 80 11 46 80 - 100 4 50

Find the mid values of each class and calculate the arithmetic mean of the given distribution. Marks Number of students 0 - 20 5 20 - 40 11 40 - 60 19 60 - 80 11 80 - 100 4

We are asked to find the mid values of each class and calculate the arithmetic mean of the given distribution. Marks Number of students 0 - 20 5 20 - 40 11 40 - 60 19 60 - 80 11 80 - 100 4 Total number of students = 5 + 11 + 19 + 11 + 4 = 50 Average or arithmetic mean = Total number of all observations Total number of frequencies But here, to find the average, we do not have the raw data. Moreover, it is difficult to find the sum of marks of 50 students. In the first class interval, we have 5 students whose marks ranges between 0 - 10 . But we don't know their exact marks. In this case, we assume all of them have the mark which is the midpoint of that class. The midpoint of a class a - b = a + b 2 So, the midpoint of 0 - 20 = 0 + 20 2 = 10 Similarly, midpoint of 20 - 40 = 20 + 40 2 = 30 The midpoint of 40 - 60 = 40 + 60 2 = 50 The midpoint of 60 - 80 = 60 + 80 2 = 70 The midpoint of 80 - 100 = 80 + 100 2 = 90 Now, we assume that all the 5 students in the class 0 - 20 got approximately 10 marks. So, the total mark of all the 5 students in that class = 10 × 5 = 50 marks The total mark of all the 11 students in the class 20 - 40 = 30 × 11 = 330 The total mark of all the 19 students in the class 40 - 60 = 50 × 19 = 950 The total mark of all the 11 students in the class 60 - 80 = 70 × 11 = 770 The total mark of all the 4 students in the class 80 - 100 = 90 × 4 = 360 We can tabulate the calculated data as follows. ∑ represents the sum of items. Marks Midpoint of class x Number of students f f x 0 - 20 10 5 50 20 - 40 30 11 330 40 - 60 50 19 950 60 - 80 70 11 770 80 - 100 90 4 360 ∑ f = 50 ∑ f x = 2460 Average or arithmetic mean = Total marks obtained by students Total number of students So, the arithmetic mean of the given data = ∑ f x ∑ f = 2460 50 = 49 . 2 Hence, the arithmetic mean is 49 . 2 .