MathsCBSE Class 10 · Basic · Board exam 2025, set 430/2/1 · 5 marks · Long answer

CBSE Class 10 Mathematics Basic 2025: question 35(b)

Set in the CBSE Class 10 board exam of 2025, paper 430/2/1, section D, question 35(b), for 5 marks. Try it first; the hints and our step-by-step solution are below.

Q35(b) · 5 marks · Long answerStatistics

A class teacher has the following absentees record of 30 students of a class. Number of days: 0-4, 4-8, 8-12, 12-16, 16-20, 20-24. Number of absent students: 1, 8, x, 6, 5, y. If the mean number of days a student was absent is 12, find the values of x and y.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2025 board paper, set 430/2/1.

Hints

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

Hint 1

Find the class mark (mid-point) of each class and multiply it by its frequency.

Hint 2

You get two equations: one from the total number of students (30) and one from the mean formula $\overset{x}{ˉ} = \sum f_{i} x_{i} / \sum f_{i}$ .

Hint 3

Solve $x + y = 10$ together with the equation from the mean by substitution.

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 the class marks $x_{i}$ and form the table:
Days $f_{i}$ $x_{i}$ $f_{i} x_{i}$
0–4 1 2 2
4–8 8 6 48
8–12 $x$ 10 $10 x$
12–16 6 14 84
16–20 5 18 90
20–24 $y$ 22 $22 y$
Total $20 + x + y$ $224 + 10 x + 22 y$
2 marks
There are 30 students in all, so $\sum f_{i} = 30$ :
$20 + x + y = 30 \Rightarrow x + y = 10 ... (1)$
1 mark
Mean $= \frac{\sum f _{i} x _{i}}{\sum f _{i}}$ , so $12 = \frac{224 + 10 x + 22 y}{30}$ .
Then $360 = 224 + 10 x + 22 y \Rightarrow 10 x + 22 y = 136 \Rightarrow 5 x + 11 y = 68 ... (2)$
1 mark
From (1), $x = 10 - y$ . Substituting in (2): $50 - 5 y + 11 y = 68 \Rightarrow 6 y = 18 \Rightarrow y = 3$
½ mark
Then $x = 10 - 3 = 7$ .
Hence $x = 7$ and $y = 3$ .
½ mark

Days	$f_{i}$	$x_{i}$	$f_{i} x_{i}$
0–4	1	2	2
4–8	8	6	48
8–12	$x$	10	$10 x$
12–16	6	14	84
16–20	5	18	90
20–24	$y$	22	$22 y$
Total	$20 + x + y$		$224 + 10 x + 22 y$

Answer: x = 7, y = 3

Where the marks are

Correct table with class marks and $f_{i} x_{i}$ , totals $20 + x + y$ and $224 + 10 x + 22 y$ (2 marks)
Forms $x + y = 10$ from total frequency 30 (1 mark)
Forms $5 x + 11 y = 68$ from mean = 12 (1 mark)
Gets $x = 7$ (½ mark)
Gets $y = 3$ (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 paper2025 board paper, set 430/2/1 (Basic): every question, by section.

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CBSE Class 10 Mathematics Basic 2025: question 35(b)

Hints

Step-by-step solution

Revise the chapter

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