Maths · Statistics and probability · chapter 13 of 14
Class 10 Maths Chapter 13: Statistics case study question with answers
One case-based question of the kind the board asks in Section E: a passage and a table, then 3 parts worth 4 marks in all, with the answer and the marking scheme for each. Written from the NCERT chapter.
Case study · 4 marks
A school in Nagpur studies the Mathematics marks of its 60 Class 10 students in the half-yearly test, to plan extra classes. The marks are grouped in classes of size 20, as in the table. The Mathematics teacher wants to know the class in which most students lie, how many students scored below 60, and a central value of the marks to report to the principal.
| Marks | Number of students |
|---|---|
| 0-20 | 8 |
| 20-40 | 10 |
| 40-60 | 20 |
| 60-80 | 10 |
| 80-100 | 12 |
Part 1 · 1 mark
The modal class of the marks is
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Answer: (b) 40-60
The largest frequency, 20, belongs to 40-60.
Part 2 · 1 mark
The number of students who scored less than 60 is
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Answer: (b) 38
Less than 60 = 8 + 10 + 20 = 38. 42 counts those scoring 40 or more.
Part 3 · 2 marks
Find the median marks.
Answer and marking scheme
Cumulative frequencies 8, 18, 38, 48, 60; n/2 = 30, so the median class is 40-60 with cf = 18, f = 20. Median = 40 + ((30 − 18) ÷ 20) × 20 = 52.
- median class 40-60 with cf = 18, f = 20 (1)
- median = 52 (1)
Or
Find the modal marks.
Answer and marking scheme
Modal class 40-60: l = 40, f₁ = 20, f₀ = 10, f₂ = 10, h = 20. Mode = 40 + ((20 − 10) ÷ (40 − 10 − 10)) × 20 = 50.
- l, f₁, f₀, f₂, h substituted (1)
- mode = 50 (1)
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