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

CBSE Class 10 Mathematics Standard 2026: question 34(a)

Set in the CBSE Class 10 board exam of 2026, paper 30/5/1, section D, question 34(a), for 5 marks. Try it first; the hints and our step-by-step solution are below.

Q34(a) · 5 marks · Long answerStatistics

The mean of the following frequency distribution is 28. If sum of all frequencies is 100, then find the values of p and q:

Class Interval	0–10	10–20	20–30	30–40	40–50	50–60
Frequency	12	p	27	20	q	6

Source: official question paper from cbse.gov.in (PDF). See it in the full 2026 board paper, set 30/5/1.

Hints

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

Hint 1

Find the class mark of each interval and the products $f_{i} x_{i}$ .

Hint 2

Use the total frequency 100 to get one equation in p and q.

Hint 3

Use mean $= \frac{\sum f _{i} x _{i}}{\sum f _{i}} = 28$ for a second equation, then solve the pair.

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.

Table of class marks and products:
Class $x_{i}$ $f_{i}$ $f_{i} x_{i}$
0–10 5 12 60
10–20 15 p 15p
20–30 25 27 675
30–40 35 20 700
40–50 45 q 45q
50–60 55 6 330
Total $65 + p + q$ $1765 + 15 p + 45 q$
2 marks
$\sum f_{i} = 100 \Rightarrow 65 + p + q = 100 \Rightarrow p + q = 35$ ...(1)
½ mark
Mean $= \frac{\sum f _{i} x _{i}}{\sum f _{i}} \Rightarrow 28 = \frac{1765 + 15 p + 45 q}{100}$
1 mark
$2800 = 1765 + 15 p + 45 q \Rightarrow 15 p + 45 q = 1035 \Rightarrow p + 3 q = 69$ ...(2)
½ mark
(2) – (1): $2 q = 34 \Rightarrow q = 17$ ; from (1), $p = 35 - 17 = 18$ .
1 mark

Class	$x_{i}$	$f_{i}$	$f_{i} x_{i}$
0–10	5	12	60
10–20	15	p	15p
20–30	25	27	675
30–40	35	20	700
40–50	45	q	45q
50–60	55	6	330
Total		$65 + p + q$	$1765 + 15 p + 45 q$

Answer: $p = 18$ , $q = 17$

Where the marks are

Correct table with $x_{i}$ , $f_{i} x_{i}$ and totals (2 marks)
$p + q = 35$ (½ mark)
Sets mean $= \frac{1765 + 15 p + 45 q}{100} = 28$ (1 mark)
$p + 3 q = 69$ (½ mark)
$p = 18$ (½ mark), $q = 17$ (½ mark)

Revise the chapter

Chapter: Statistics (notes, formulas, where marks are lost and every past question)

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 30/5/1 (Standard): every question, by section.

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CBSE Class 10 Mathematics Standard 2026: question 34(a)

Hints

Step-by-step solution

Revise the chapter

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