Find the mean using the step deviation method. Class 0-10 10-20 20-30 30-40 40-50 --- --- --- --- --- --- Frequency 6 10 15 9 10

MathsCBSE Class 10 · Basic · Sample paper, session 2024-25 · 3 marks · Short answer

CBSE Class 10 Mathematics Basic sample paper 2024-25: question 29

From the official CBSE sample question paper for 2024-25, section C, question 29, for 3 marks. Try it first; the hints and our step-by-step solution are below.

Q29 · 3 marks · Short answerStatistics

Find the mean using the step deviation method.

Class	0-10	10-20	20-30	30-40	40-50
Frequency	6	10	15	9	10

Source: official sample paper from cbseacademic.nic.in (PDF). See it in the full Sample paper 2024-25.

Hints

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

Hint 1

Find the class marks, then take the middle one (25) as the assumed mean.

Hint 2

Use $u_{i} = \frac{x _{i} - a}{h}$ and Mean $= a + h \frac{Σ f _{i} u _{i}}{Σ f _{i}}$ .

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 $a = 25$ and class size $h = 10$ , with $u_{i} = \frac{x _{i} - 25}{10}$ .
Class $x_{i}$ $f_{i}$ $u_{i}$ $f_{i} u_{i}$
0-10 5 6 −2 −12
10-20 15 10 −1 −10
20-30 25 15 0 0
30-40 35 9 1 9
40-50 45 10 2 20
Total $Σ f_{i} = 50$ $Σ f_{i} u_{i} = 7$
1½ marks
Mean $= a + h \times \frac{Σ f _{i} u _{i}}{Σ f _{i}} = 25 + 10 \times \frac{7}{50}$
1 mark
$= 25 + 1.4 = 26.4$
½ mark

Class	$x_{i}$	$f_{i}$	$u_{i}$	$f_{i} u_{i}$
0-10	5	6	−2	−12
10-20	15	10	−1	−10
20-30	25	15	0	0
30-40	35	9	1	9
40-50	45	10	2	20
Total		$Σ f_{i} = 50$		$Σ f_{i} u_{i} = 7$

Answer: Mean = 26.4

Where the marks are

Correct table with $x_{i}$ , $u_{i}$ , $f_{i} u_{i}$ , $Σ f_{i} = 50$ and $Σ f_{i} u_{i} = 7$ (1½ marks)
Correct substitution in the step-deviation formula (1 mark)
Mean = 26.4 (½ mark)

Revise the chapter

Chapter: Statistics (notes, formulas, where marks are lost and every past question)
Topic: Step Deviation 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 2024-25 (Basic): every question, by section.

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CBSE Class 10 Mathematics Basic sample paper 2024-25: question 29

Hints

Step-by-step solution

Revise the chapter

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