MathsCBSE Class 10 · Standard · Board exam 2026, set 30/2/1 · 5 marks · Long answer

CBSE Class 10 Mathematics Standard 2026: question 35

Set in the CBSE Class 10 board exam of 2026, paper 30/2/1, section D, question 35, for 5 marks. Try it first; the hints and our step-by-step solution are below.

Q35 · 5 marks · Long answerCompetency-basedStatistics

An SBI health insurance agent found the following data for distribution of ages of 100 policy holders. The health insurance policies are given to persons of age 15 years and onwards, but less than 60 years.

Age (in yrs)	Number of policy holders
15 – 20	2
20 – 25	4
25 – 30	18
30 – 35	21
35 – 40	33
40 – 45	11
45 – 50	3
50 – 55	6
55 – 60	2

Find the modal age and median age of the policy holders.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2026 board paper, set 30/2/1.

Hints

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

Hint 1

The modal class has the highest frequency; the median class is where cf first passes n/2.

Hint 2

Mode $= l + \frac{f _{1} - f _{0}}{2 f _{1} - f _{0} - f _{2}} h$ and Median $= l + \frac{n /2 - c f}{f} h$ .

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.

Cumulative frequency table:
Age f cf
15–20 2 2
20–25 4 6
25–30 18 24
30–35 21 45
35–40 33 78
40–45 11 89
45–50 3 92
50–55 6 98
55–60 2 100
$n = 100$
1 mark
Highest frequency is 33, so modal class = 35–40; $l = 35, f_{1} = 33, f_{0} = 21, f_{2} = 11, h = 5$
½ mark
Mode $= l + \frac{f _{1} - f _{0}}{2 f _{1} - f _{0} - f _{2}} \times h = 35 + \frac{33 - 21}{66 - 21 - 11} \times 5$
1 mark
$= 35 + \frac{60}{34} = \frac{625}{17} \approx 36.76$ years
½ mark
$\frac{n}{2} = 50$ ; cf just greater than 50 is 78, so median class = 35–40; $l = 35, c f = 45, f = 33, h = 5$
½ mark
Median $= l + \frac{\frac{n}{2} - c f}{f} \times h = 35 + \frac{50 - 45}{33} \times 5$
1 mark
$= 35 + \frac{25}{33} = \frac{1180}{33} \approx 35.76$ years
½ mark

Age	f	cf
15–20	2	2
20–25	4	6
25–30	18	24
30–35	21	45
35–40	33	78
40–45	11	89
45–50	3	92
50–55	6	98
55–60	2	100

Answer: Modal age ≈ 36.76 years; median age ≈ 35.76 years

Where the marks are

Correct cumulative frequency table (1 mark)
Identifies modal class 35–40 (½ mark)
Substitutes correctly in mode formula (1 mark)
Mode = 625/17 ≈ 36.76 years (½ mark)
Identifies median class 35–40 using n/2 = 50 (½ mark)
Substitutes correctly in median formula (1 mark)
Median = 1180/33 ≈ 35.76 years (½ mark)

Revise the chapter

Chapter: Statistics (notes, formulas, where marks are lost and every past question)

Practise this chapterBoard-style questions from Statistics, one at a time, marked against the answer key and marking points.Back to the full paper2026 board paper, set 30/2/1 (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 2026: question 35

Hints

Step-by-step solution

Revise the chapter

More questions from Statistics