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.

MathsCBSE Class 10 · Basic · Board exam 2026, set 430/2/1 · 5 marks · Long answer

CBSE Class 10 Mathematics Basic 2026: question 35(b)

Set in the CBSE Class 10 board exam of 2026, 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 answerCompetency-basedStatistics

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 2026 board paper, set 430/2/1.

Hints

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

Hint 1

The frequencies must add up to 30; this gives one equation.

Hint 2

Find the class marks (mid-points) and the products $f_{i} x_{i}$ .

Hint 3

Set $Σ f_{i} x_{i} /30 = 12$ for the second equation, then solve the two together.

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.

Total number of students: $1 + 8 + x + 6 + 5 + y = 30 \Rightarrow x + y = 10$ ...(1).
1 mark
Class marks $x_{i}$ : 2, 6, 10, 14, 18, 22. Products $f_{i} x_{i}$ : 2, 48, $10 x$ , 84, 90, $22 y$ . So $Σ f_{i} x_{i} = 224 + 10 x + 22 y$ .
2 marks
Mean $= \frac{Σ f _{i} x _{i}}{Σ f _{i}}$ : $\frac{224 + 10 x + 22 y}{30} = 12 \Rightarrow 10 x + 22 y = 136 \Rightarrow 5 x + 11 y = 68$ ...(2).
1 mark
From (1), $x = 10 - y$ . Substituting in (2): $50 - 5 y + 11 y = 68 \Rightarrow 6 y = 18 \Rightarrow y = 3$ , and then $x = 7$ .
1 mark

Answer: x = 7, y = 3

Where the marks are

Forms $x + y = 10$ from the total (1 mark)
Finds the class marks and $Σ f_{i} x_{i} = 224 + 10 x + 22 y$ (2 marks)
Uses mean = 12 to form $5 x + 11 y = 68$ (1 mark)
Solves to get $x = 7$ , $y = 3$ (1 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 430/2/1 (Basic): every question, by section.

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CBSE Class 10 Mathematics Basic 2026: question 35(b)

Hints

Step-by-step solution

Revise the chapter

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