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 standard deviation ?

Step-by-step solution

The total number of students is 100 . 10 + 20 + f + 40 = 100 f = 30 The mid-points of the class intervals are x_i = 5, 15, 25, 35 . The mean x is given by: x = f_i x_i f_i = 10(5) + 20(15) + 30(25) + 40(35) 100 x = 50 + 300 + 750 + 1400 100 = 2500 100 = 25 The variance ^2 is given by: ^2 = f_i (x_i - x )^2 f_i ^2 = 10(5 - 25)^2 + 20(15 - 25)^2 + 30(25 - 25)^2 + 40(35 - 25)^2 100 ^2 = 10(-20)^2 + 20(-10)^2 + 30(0)^2 + 40(10)^2 100 ^2 = 10(400) + 20(100) + 0 + 40(100) 100 ^2 = 4000 + 2000 + 0 + 4000 100 = 10000 100 =