MathsCBSE Class 10 · Basic · Board exam 2025, set 430/4/1 · 5 marks · Long answer

CBSE Class 10 Mathematics Basic 2025: question 33

Set in the CBSE Class 10 board exam of 2025, paper 430/4/1, section D, question 33, for 5 marks. Try it first; the hints and our step-by-step solution are below.

Q33 · 5 marks · Long answerStatistics

Find 'mean' and 'mode' of the following data:

Source: official question paper from cbse.gov.in (PDF). See it in the full 2025 board paper, set 430/4/1.

Hints

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

Hint 1

Find the class marks, then use the step-deviation method with assumed mean 27.5.

Hint 2

For the mode, first pick the class with the highest frequency.

Hint 3

Use mode $= l + \frac{f _{1} - f _{0}}{2 f _{1} - f _{0} - f _{2}} \times h$ with $f_{0}$ and $f_{2}$ the frequencies of the neighbouring classes.

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.

Take assumed mean $a = 27.5$ , $h = 5$ , $u_{i} = \frac{x _{i} - 27.5}{5}$ .
Class $x_{i}$ $f_{i}$ $u_{i}$ $f_{i} u_{i}$
15–20 17.5 6 −2 −12
20–25 22.5 16 −1 −16
25–30 27.5 17 0 0
30–35 32.5 4 1 4
35–40 37.5 5 2 10
40–45 42.5 2 3 6
$\sum f_{i} = 50$ $\sum f_{i} u_{i} = - 8$
1½ marks
Mean $= a + \frac{\sum f _{i} u _{i}}{\sum f _{i}} \times h = 27.5 + \frac{- 8}{50} \times 5$
1 mark
$= 27.5 - 0.8 = 26.7$
½ mark
The highest frequency is 17, so the modal class is 25–30: $l = 25$ , $f_{1} = 17$ , $f_{0} = 16$ , $f_{2} = 4$ , $h = 5$ . Mode $= l + \frac{f _{1} - f _{0}}{2 f _{1} - f _{0} - f _{2}} \times h = 25 + \frac{17 - 16}{34 - 16 - 4} \times 5$
1½ marks
$= 25 + \frac{5}{14} \approx 25 + 0.36 = 25.36$
½ mark

Class	$x_{i}$	$f_{i}$	$u_{i}$	$f_{i} u_{i}$
15–20	17.5	6	−2	−12
20–25	22.5	16	−1	−16
25–30	27.5	17	0	0
30–35	32.5	4	1	4
35–40	37.5	5	2	10
40–45	42.5	2	3	6
		$\sum f_{i} = 50$		$\sum f_{i} u_{i} = - 8$

Answer: Mean $= 26.7$ ; Mode $\approx 25.36$

Where the marks are

Correct table with $\sum f_{i} = 50$ and $\sum f_{i} u_{i} = - 8$ (1½ marks)
Correct substitution in the mean formula (1 mark)
Mean $= 26.7$ (½ mark)
Identifies the modal class 25–30 and substitutes in the mode formula (1½ marks)
Mode $\approx 25.36$ (½ mark)

Revise the chapter

Chapter: Statistics (notes, formulas, where marks are lost and every past question)
Topic: Relation Between Mean, Median and Mode

Practise this chapterBoard-style questions from Statistics, one at a time, marked against the answer key and marking points.Back to the full paper2025 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 2025: question 33

Hints

Step-by-step solution

Revise the chapter

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