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Chapter: Statistics· Mathematics Part 1 (Algebra)

Asked in: July 2024 board paperQ.10 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) Pr…

Asked in: July 2024 board paper

Q.10 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 distribution table.
(b) Find the mode of the marks scored.

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

(a) The percentages given add to 10 + 20 + 35 + 20 = 85%, so the remaining 30 students are 15% of the group.

Total students = \(\dfrac{30 \times 100}{15} = 200\)

MarksNo. of students
0–2010% of 200 = 20
20–4020% of 200 = 40
40–6035% of 200 = 70
60–8020% of 200 = 40
80–10030
Total200

(b) Modal class = 40–60. L = 40, \(f_1 = 70\), \(f_0 = 40\), \(f_2 = 40\), h = 20

\(\text{Mode} = L + \left[ \dfrac{f_1 - f_0}{2f_1 - f_0 - f_2} \right] \times h\)

\(= 40 + \left[ \dfrac{70 - 40}{140 - 40 - 40} \right] \times 20 = 40 + \dfrac{30}{60} \times 20 = 40 + 10 = 50\)

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