Passage: The frequency distribution of marks obtained by 100 students in a certain subject is given below : Marks 0 - 10 10 - 20 20 - 30 30 - 40 No. of students 10 20 f 40 Question: What is the mean deviation about the arithmetic mean ?

Step-by-step solution

Total number of students is 100 . 10 + 20 + f + 40 = 100 f = 30 The mid-points x_i of the classes are 5, 15, 25, 35 . The arithmetic mean x = f_i x_i f_i x = 10 5 + 20 15 + 30 25 + 40 35 100 x = 50 + 300 + 750 + 1400 100 = 2500 100 = 25 The absolute deviations |x_i - x | are |5 - 25| = 20 , |15 - 25| = 10 , |25 - 25| = 0 , and |35 - 25| = 10 . Mean deviation about the mean = f_i |x_i - x | f_i = 10 20 + 20 10 + 30 0 + 40 10 100 = 200 + 200 + 0 + 400 100 = 800 100 = 8 Answer: 8