MathsCBSE Class 10 · Standard · Board exam 2024, set 30/5/1 · 4 marks · Case-based

CBSE Class 10 Mathematics Standard 2024: question 38

Set in the CBSE Class 10 board exam of 2024, paper 30/5/1, section E, question 38, for 4 marks. Try it first; the hints and our step-by-step solution are below.

Q38 · 4 marks · Case-basedCompetency-basedStatistics

Case Study – 3

Activities like running or cycling reduce stress and the risk of mental disorders like depression. Running helps build endurance. Children develop stronger bones and muscles and are less prone to gain weight. The physical education teacher of a school has decided to conduct an inter school running tournament in his school premises. The time taken by a group of students to run 100 m, was noted as follows :

Time (in seconds)	0 – 20	20 – 40	40 – 60	60 – 80	80 – 100
Number of students	8	10	13	6	3

Based on the above, answer the following questions :

(i)
What is the median class of the above given data ?
1 mark
(ii)(a)
Find the mean time taken by the students to finish the race.
2 marks
OR
(ii)(b)
Find the mode of the above given data.
2 marks
(iii)
How many students took time less than 60 seconds ?
1 mark

Figure in the paper: A photograph, taken from above, of runners starting a 100 m race on a red athletics track with white lane lines and a starting line; the runners are in their starting positions. See it in the official paper.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2024 board paper, set 30/5/1.

Hints

Open one hint at a time and try again before the next.

Hint 1

For the median class, find $N /2$ and look at the cumulative frequencies.

Hint 2

For the mean, use the class marks $x_{i}$ and compute $\sum f_{i} x_{i} / \sum f_{i}$ . For the mode, use $l + \frac{f _{1} - f _{0}}{2 f _{1} - f _{0} - f _{2}} \times h$ on the class with the highest frequency.

Hint 3

For (iii), add the frequencies of all classes below 60.

Step-by-step solution

Each step shows the marks it earns, as an examiner would award them. Checked by an independent re-solve from the question paper.

(i) The cumulative frequencies are 8, 18, 31, 37, 40, so $N = 40$ and $\frac{N}{2} = 20$ .
½ mark
(i) The first cf greater than 20 is 31, for class 40–60. So the median class is 40–60.
½ mark
(ii)(a) Class marks $x_{i}$ are 10, 30, 50, 70, 90. The products $f_{i} x_{i}$ are $8 \times 10 = 80$ , $10 \times 30 = 300$ , $13 \times 50 = 650$ , $6 \times 70 = 420$ and $3 \times 90 = 270$ . So $\sum f_{i} = 40$ and $\sum f_{i} x_{i} = 1720$ .
1½ marks
(ii)(a) Mean $= \frac{\sum f _{i} x _{i}}{\sum f _{i}} = \frac{1720}{40} = 43$ seconds.
½ mark
(ii)(b) The highest frequency is 13, so the modal class is 40–60. Here $l = 40$ , $f_{1} = 13$ , $f_{0} = 10$ , $f_{2} = 6$ , $h = 20$ .
½ mark
(ii)(b) Mode $= l + \frac{f _{1} - f _{0}}{2 f _{1} - f _{0} - f _{2}} \times h = 40 + \frac{13 - 10}{26 - 10 - 6} \times 20$
1 mark
(ii)(b) $= 40 + \frac{3}{10} \times 20 = 46$ seconds.
½ mark
(iii) Students taking less than 60 s $= 8 + 10 + 13 = 31$ (the cf up to 60). So 31 students.
1 mark

Answer: (i) 40–60; (ii)(a) Mean = 43 s; (ii)(b) Mode = 46 s; (iii) 31 students

Where the marks are

(i) Correct cumulative frequencies (½ mark)
(i) Median class 40–60 (½ mark)
(ii)(a) Correct table of $x_{i}$ and $f_{i} x_{i}$ with $\sum f_{i} x_{i} = 1720$ (1½ marks)
(ii)(a) Mean $= 1720/40 = 43$ (½ mark)
(ii)(b) Modal class 40–60 (½ mark)
(ii)(b) Correct substitution in the mode formula (1 mark)
(ii)(b) Mode = 46 (½ mark)
(iii) 31 students (1 mark)

Revise the chapter

Chapter: Statistics (notes, formulas, where marks are lost and every past question)
Topic: Median of Grouped Data

Practise this chapterBoard-style questions from Statistics, one at a time, marked against the answer key and marking points.Back to the full paper2024 board paper, set 30/5/1 (Standard): every question, by section.

The question is transcribed from the official paper; figures are described in words. The solution, hints and chapter tag are ours. Spotted an error? Write tosupport@questionbuddy.in.

CBSE Class 10 Mathematics Standard 2024: question 38

Hints

Step-by-step solution

Revise the chapter

More questions from Statistics