In one group of students; 10% students got 0 to 20 marks; 20% students got 20 to 40 marks; 35% students got 40 to 60 marks; 20% students got 60 to 80 marks and remaining 30 students got 80 to 100 marks, then :(a) Prepare a grouped frequency distribut…

Answer: (a) total 200 students, frequencies 20, 40, 70, 40, 30; (b) Mode = 50 marks

(a) The percentages given add up to \(10 + 20 + 35 + 20 = 85\%\), so the remaining 15% got 80 to 100 marks.

15% of total = 30 students, so the total number of students \(= \dfrac{30 \times 100}{15} = 200\).

(b) The maximum frequency is 70, so the modal class is 40—60 : \(L = 40\), \(f_1 = 70\), \(f_0 = 40\), \(f_2 = 40\), \(h = 20\).

Mode \(= L + \left(\dfrac{f_1 - f_0}{2f_1 - f_0 - f_2}\right)h = 40 + \dfrac{70 - 40}{140 - 40 - 40} \times 20\)

\(= 40 + \dfrac{30}{60} \times 20 = 40 + 10 = 50\).

The mode of the marks is 50.