Find the mean of the following frequency distribution : Classes 25–30 30–35 35–40 40–45 45–50 50–55 55–60 --- --- --- --- --- --- --- --- Frequency 14 22 16 6 5 3 4

MathsCBSE Class 10 · Standard · Board exam 2023, set 30/5/1 · 3 marks · Short answer

CBSE Class 10 Mathematics Standard 2023: question 31

Set in the CBSE Class 10 board exam of 2023, paper 30/5/1, section C, question 31, for 3 marks. Try it first; the hints and our step-by-step solution are below.

Q31 · 3 marks · Short answerStatistics

Find the mean of the following frequency distribution :

Classes	25–30	30–35	35–40	40–45	45–50	50–55	55–60
Frequency	14	22	16	6	5	3	4

Source: official question paper from cbse.gov.in (PDF). See it in the full 2023 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 class first: (lower limit + upper limit)/2.

Hint 2

Choose a middle class mark like 42.5 as the assumed mean and divide deviations by the class size 5.

Hint 3

Use $\overset{x}{ˉ} = a + \frac{Σ f _{i} u _{i}}{Σ f _{i}} \times h$ .

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 $a = 42.5$ , class size $h = 5$ , $u_{i} = \frac{x _{i} - 42.5}{5}$ .
Class $x_{i}$ $f_{i}$ $u_{i}$ $f_{i} u_{i}$
25–30 27.5 14 −3 −42
30–35 32.5 22 −2 −44
35–40 37.5 16 −1 −16
40–45 42.5 6 0 0
45–50 47.5 5 1 5
50–55 52.5 3 2 6
55–60 57.5 4 3 12
Total $Σ f_{i} = 70$ $Σ f_{i} u_{i} = - 79$
2 marks
Mean $\overset{x}{ˉ} = a + \frac{Σ f _{i} u _{i}}{Σ f _{i}} \times h = 42.5 + \frac{- 79}{70} \times 5 = 42.5 - 5.64 = 36.86$ (approx.)
1 mark

Class	$x_{i}$	$f_{i}$	$u_{i}$	$f_{i} u_{i}$
25–30	27.5	14	−3	−42
30–35	32.5	22	−2	−44
35–40	37.5	16	−1	−16
40–45	42.5	6	0	0
45–50	47.5	5	1	5
50–55	52.5	3	2	6
55–60	57.5	4	3	12
Total		$Σ f_{i} = 70$		$Σ f_{i} u_{i} = - 79$

Answer: Mean ≈ 36.86

Where the marks are

Correct table of class marks, uᵢ and fᵢuᵢ with Σfᵢ = 70 and Σfᵢuᵢ = −79 (2 marks)
Applies step-deviation formula to get mean ≈ 36.86 (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 paper2023 board paper, set 30/5/1 (Standard): every question, by section.

The question is transcribed from the official paper; figures are described in words. The solution, hints and chapter tag are ours. Spotted an error? Write tosupport@questionbuddy.in.

CBSE Class 10 Mathematics Standard 2023: question 31

Hints

Step-by-step solution

Revise the chapter

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