MathsCBSE Class 10 · Basic · Sample paper, session 2026-27 · 3 marks · Short answer

CBSE Class 10 Mathematics Basic sample paper 2026-27: question 30(A)

From the official CBSE sample question paper for 2026-27, section C, question 30(A), for 3 marks. Try it first; the hints and our step-by-step solution are below.

Q30(A) · 3 marks · Short answerStatistics

The mean of the following distribution is 48 and sum of all the frequencies is 50. Find the missing frequencies $x$ and $y$ .

Class	20-30	30-40	40-50	50-60	60-70
Frequency	8	6	$x$	11	$y$

Source: official sample paper from cbseacademic.nic.in (PDF). See it in the full Sample paper 2026-27.

Hints

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

Hint 1

Use the total frequency 50 to get one equation in x and y.

Hint 2

Use the step-deviation mean formula with assumed mean 45 to get a second equation.

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 $a = 45$ , $h = 10$ , $u_{i} = \frac{x _{i} - 45}{10}$ :
Class $f_{i}$ $x_{i}$ $u_{i}$ $f_{i} u_{i}$
20-30 8 25 −2 −16
30-40 6 35 −1 −6
40-50 x 45 0 0
50-60 11 55 1 11
60-70 y 65 2 2y
Total 25 + x + y 2y − 11
1 mark
$\sum f_{i} = 50 \Rightarrow 25 + x + y = 50 \Rightarrow x + y = 25$ ...(1)
½ mark
Mean $= a + \frac{\sum f _{i} u _{i}}{\sum f _{i}} \times h$ , so $48 = 45 + \frac{2 y - 11}{50} \times 10$
½ mark
$3 = \frac{2 y - 11}{5} \Rightarrow 2 y = 26 \Rightarrow y = 13$
½ mark
From (1), $x = 25 - 13 = 12$
½ mark

Class	$f_{i}$	$x_{i}$	$u_{i}$	$f_{i} u_{i}$
20-30	8	25	−2	−16
30-40	6	35	−1	−6
40-50	x	45	0	0
50-60	11	55	1	11
60-70	y	65	2	2y
Total	25 + x + y			2y − 11

Answer: $x = 12$ , $y = 13$

Where the marks are

Correct table with $f_{i} u_{i}$ total $2 y - 11$ (1 mark)
Forms $x + y = 25$ (½ mark)
Substitutes in the mean formula (½ mark)
y = 13 (½ mark)
x = 12 (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 paperSample paper 2026-27 (Basic): every question, by section.

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CBSE Class 10 Mathematics Basic sample paper 2026-27: question 30(A)

Hints

Step-by-step solution

Revise the chapter

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