MathsCBSE Class 10 · Basic · Board exam 2024, set 430/4/1 · 4 marks · Case-based

CBSE Class 10 Mathematics Basic 2024: question 36

Set in the CBSE Class 10 board exam of 2024, paper 430/4/1, section E, question 36, for 4 marks. Try it first; the hints and our step-by-step solution are below.

Q36 · 4 marks · Case-basedCompetency-basedStatistics

Case Study – 1

Mutual Fund : A mutual fund is a type of investment vehicle that pools money from multiple investors to invest in securities like stocks, bonds or other securities. Mutual funds are operated by professional money managers, who allocate the fund's assets and attempt to produce capital gains or income for the fund's investors.

Net Asset Value (NAV) represents a fund's per share market value. It is the price at which the investors buy fund shares from a fund company and sell them to a fund company.

The following table shows the Net Asset Value (NAV) per unit of mutual fund of ICICI mutual funds :

NAV (in ₹)	0 – 5	5 – 10	10 – 15	15 – 20	20 – 25
Number of mutual funds	13	16	22	18	11

Based on the above information, answer the following questions :

(i)
What is the upper limit of modal class of the data ?
1 mark
(ii)
What is the median class of the data ?
1 mark
(iii)(a)
What is the mode NAV of mutual funds ?
2 marks
OR
(iii)(b)
What is the median NAV of mutual funds ?
2 marks

Source: official question paper from cbse.gov.in (PDF). See it in the full 2024 board paper, set 430/4/1.

Hints

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

Hint 1

The modal class is the class with the highest frequency. For the median class, find $N /2$ and look at the cumulative frequencies.

Hint 2

For the mode, use $l + \frac{f _{1} - f _{0}}{2 f _{1} - f _{0} - f _{2}} \times h$ , where $f_{0}$ and $f_{2}$ are the frequencies of the classes before and after the modal class.

Hint 3

For the median, use $l + \frac{N /2 - c f}{f} \times h$ , where $c f$ is the cumulative frequency of the class just before the median class.

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 highest frequency is 22, in the class 10 – 15, so 10 – 15 is the modal class.
Its upper limit is 15.
1 mark
(ii) Total frequency $N = 13 + 16 + 22 + 18 + 11 = 80$ , so $\frac{N}{2} = 40$ .
The cumulative frequencies are 13, 29, 51, 69, 80. The first cf greater than 40 is 51, so the median class is 10 – 15.
1 mark
(iii)(a) For the modal class 10 – 15: $l = 10$ , $f_{1} = 22$ , $f_{0} = 16$ , $f_{2} = 18$ , $h = 5$ .
$Mode = l + (\frac{f _{1} - f _{0}}{2 f _{1} - f _{0} - f _{2}}) h = 10 + (\frac{22 - 16}{44 - 16 - 18}) \times 5$
1½ marks
$= 10 + \frac{6}{10} \times 5 = 10 + 3 = 13$
The mode NAV is ₹ 13.
½ mark
(iii)(b) Cumulative frequency table:
NAV (₹) f cf
0 – 5 13 13
5 – 10 16 29
10 – 15 22 51
15 – 20 18 69
20 – 25 11 80
½ mark
For the median class 10 – 15: $l = 10$ , $\frac{N}{2} = 40$ , $c f = 29$ , $f = 22$ , $h = 5$ .
$Median = l + (\frac{\frac{N}{2} - c f}{f}) h = 10 + (\frac{40 - 29}{22}) \times 5$
1 mark
$= 10 + \frac{11}{22} \times 5 = 10 + 2.5 = 12.5$
The median NAV is ₹ 12.5.
½ mark

NAV (₹)	f	cf
0 – 5	13	13
5 – 10	16	29
10 – 15	22	51
15 – 20	18	69
20 – 25	11	80

Answer: (i) 15; (ii) 10 – 15; (iii)(a) Mode = ₹ 13; (iii)(b) Median = ₹ 12.5

Where the marks are

(i) Upper limit of the modal class is 15 (1 mark)
(ii) Median class is 10 – 15 (1 mark)
(iii)(a) Correct values substituted in the mode formula (1½ marks)
(iii)(a) Mode = 13 (½ mark)
(iii)(b) Correct cumulative frequency table (½ mark)
(iii)(b) Correct values substituted in the median formula (1 mark)
(iii)(b) Median = 12.5 (½ mark)

Revise the chapter

Chapter: Statistics (notes, formulas, where marks are lost and every past question)
Topic: Mode 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 430/4/1 (Basic): 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 Basic 2024: question 36

Hints

Step-by-step solution

Revise the chapter

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