MathsCBSE Class 10 · Standard · Board exam 2026, set 30/3/1 · 5 marks · Long answer

CBSE Class 10 Mathematics Standard 2026: question 32(b)

Set in the CBSE Class 10 board exam of 2026, paper 30/3/1, section D, question 32(b), for 5 marks. Try it first; the hints and our step-by-step solution are below.

Q32(b) · 5 marks · Long answerStatistics

Find mean and mode of the following distribution :

Source: official question paper from cbse.gov.in (PDF). See it in the full 2026 board paper, set 30/3/1.

Hints

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

Hint 1

For the mean, use the step-deviation method with assumed mean 35 and h = 10.

Hint 2

For the mode, the modal class has the highest frequency (13). Use $l + \frac{f _{1} - f _{0}}{2 f _{1} - f _{0} - f _{2}} \times h$ .

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.

Step-deviation table with $a = 35$ , $h = 10$ , $u_{i} = \frac{x _{i} - 35}{10}$ :
Class $x_{i}$ $f_{i}$ $u_{i}$ $f_{i} u_{i}$
0–10 5 3 −3 −9
10–20 15 6 −2 −12
20–30 25 11 −1 −11
30–40 35 10 0 0
40–50 45 13 1 13
50–60 55 3 2 6
60–70 65 4 3 12
Total 50 −1
2 marks
Mean $= a + \frac{\sum f _{i} u _{i}}{\sum f _{i}} \times h = 35 + \frac{- 1}{50} \times 10 = 35 - 0.2 = 34.8$
1 mark
The highest frequency is 13, so the modal class is 40–50, with:
- $l = 40$
- $f_{1} = 13$
- $f_{0} = 10$
- $f_{2} = 3$
- $h = 10$
½ mark
Mode $= l + (\frac{f _{1} - f _{0}}{2 f _{1} - f _{0} - f _{2}}) \times h = 40 + (\frac{13 - 10}{26 - 10 - 3}) \times 10 = 40 + \frac{30}{13}$
1 mark
$\approx 42.3$
½ mark

Class	$x_{i}$	$f_{i}$	$u_{i}$	$f_{i} u_{i}$
0–10	5	3	−3	−9
10–20	15	6	−2	−12
20–30	25	11	−1	−11
30–40	35	10	0	0
40–50	45	13	1	13
50–60	55	3	2	6
60–70	65	4	3	12
Total		50		−1

Answer: Mean = 34.8; Mode ≈ 42.3

Where the marks are

Correct table with $\sum f_{i} = 50$ and $\sum f_{i} u_{i} = - 1$ (2 marks)
Mean = 34.8 (1 mark)
Identifies the modal class 40–50 (½ mark)
Substitutes correctly in the mode formula (1 mark)
Mode ≈ 42.3 (½ mark)

Revise the chapter

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

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 30/3/1 (Standard): every question, by section.

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CBSE Class 10 Mathematics Standard 2026: question 32(b)

Hints

Step-by-step solution

Revise the chapter

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