If the mean of the following distribution is 54, find the value of p. Class Interval 0 – 20 20 – 40 40 – 60 60 – 80 80 – 100 --- --- --- --- --- --- Frequency 7 p 10 9 13

MathsCBSE Class 10 · Basic · Sample paper, session 2025-26 · 3 marks · Short answer

CBSE Class 10 Mathematics Basic sample paper 2025-26: question 27(B)

From the official CBSE sample question paper for 2025-26, section C, question 27(B), for 3 marks. Try it first; the hints and our step-by-step solution are below.

Q27(B) · 3 marks · Short answerStatistics

If the mean of the following distribution is 54, find the value of $p$ .

Class Interval	0 – 20	20 – 40	40 – 60	60 – 80	80 – 100
Frequency	7	$p$	10	9	13

Source: official sample paper from cbseacademic.nic.in (PDF). See it in the full Sample paper 2025-26.

Hints

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

Hint 1

Find class marks and use the step-deviation (or assumed mean) method.

Hint 2

Set the mean formula equal to 54; $\sum f_{i}$ will contain $p$ .

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 $A = 30$ , $h = 20$ , $u_{i} = \frac{x _{i} - 30}{20}$ .
Class $f_{i}$ $x_{i}$ $u_{i}$ $f_{i} u_{i}$
0–20 7 10 −1 −7
20–40 $p$ 30 0 0
40–60 10 50 1 10
60–80 9 70 2 18
80–100 13 90 3 39
Total $39 + p$ 60
2 marks
Mean $= A + \frac{\sum f _{i} u _{i}}{\sum f _{i}} \times h \Rightarrow 54 = 30 + \frac{60}{39 + p} \times 20 \Rightarrow \frac{1200}{39 + p} = 24 \Rightarrow 39 + p = 50 \Rightarrow p = 11$
1 mark

Class	$f_{i}$	$x_{i}$	$u_{i}$	$f_{i} u_{i}$
0–20	7	10	−1	−7
20–40	$p$	30	0	0
40–60	10	50	1	10
60–80	9	70	2	18
80–100	13	90	3	39
Total	$39 + p$			60

Answer: $p = 11$

Where the marks are

Correct table with $\sum f_{i} = 39 + p$ and $\sum f_{i} u_{i} = 60$ (2 marks)
Forms the mean equation and gets $p = 11$ (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 paperSample paper 2025-26 (Basic): every question, by section.

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CBSE Class 10 Mathematics Basic sample paper 2025-26: question 27(B)

Hints

Step-by-step solution

Revise the chapter

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