The following data gives the information on the observed lifetime (in hours) of 200 electrical components : Lifetime (in hours) Number of electrical components --- --- 0 – 20 10 20 – 40 35 40 – 60 50 60 – 80 60 80 – 100 30 100 – 120 15 Find the mean lifetime (in hours) of the electrical components.

MathsCBSE Class 10 · Basic · Board exam 2025, set 430/1/1 · 5 marks · Long answer

CBSE Class 10 Mathematics Basic 2025: question 35

Set in the CBSE Class 10 board exam of 2025, paper 430/1/1, section D, question 35, for 5 marks. Try it first; the hints and our step-by-step solution are below.

Q35 · 5 marks · Long answerStatistics

The following data gives the information on the observed lifetime (in hours) of 200 electrical components :

Lifetime (in hours)	Number of electrical components
0 – 20	10
20 – 40	35
40 – 60	50
60 – 80	60
80 – 100	30
100 – 120	15

Find the mean lifetime (in hours) of the electrical components.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2025 board paper, set 430/1/1.

Hints

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

Hint 1

First find the class mark (mid-point) of each class interval.

Hint 2

Choose a middle class mark, such as 50, as the assumed mean and use $u_{i} = (x_{i} - a) / h$ with $h = 20$ .

Hint 3

Mean $= a + \frac{\sum f _{i} u _{i}}{\sum f _{i}} \times h$ . Find $\sum f_{i} u_{i}$ from your table.

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.

Use the step-deviation method. Take the assumed mean $a = 50$ and class size $h = 20$ , so $u_{i} = \frac{x _{i} - 50}{20}$ .
Lifetime $x_{i}$ $f_{i}$ $u_{i}$ $f_{i} u_{i}$
0 – 20 10 10 –2 –20
20 – 40 30 35 –1 –35
40 – 60 50 50 0 0
60 – 80 70 60 1 60
80 – 100 90 30 2 60
100 – 120 110 15 3 45
Total $\sum f_{i} = 200$ $\sum f_{i} u_{i} = 110$
2 marks
Apply the formula:
$\overset{x}{ˉ} = a + \frac{\sum f _{i} u _{i}}{\sum f _{i}} \times h = 50 + \frac{110}{200} \times 20$
2 marks
$\overset{x}{ˉ} = 50 + 11 = 61$
So the mean lifetime of the electrical components is 61 hours.
1 mark

Lifetime	$x_{i}$	$f_{i}$	$u_{i}$	$f_{i} u_{i}$
0 – 20	10	10	–2	–20
20 – 40	30	35	–1	–35
40 – 60	50	50	0	0
60 – 80	70	60	1	60
80 – 100	90	30	2	60
100 – 120	110	15	3	45
Total		$\sum f_{i} = 200$		$\sum f_{i} u_{i} = 110$

Answer: Mean lifetime = 61 hours

Where the marks are

Correct table with class marks $x_{i}$ , $u_{i}$ and $f_{i} u_{i}$ , giving $\sum f_{i} = 200$ and $\sum f_{i} u_{i} = 110$ (2 marks)
Substitutes correctly into $\overset{x}{ˉ} = a + \frac{\sum f _{i} u _{i}}{\sum f _{i}} \times h$ (2 marks)
Obtains mean = 61 hours (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 paper2025 board paper, set 430/1/1 (Basic): every question, by section.

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CBSE Class 10 Mathematics Basic 2025: question 35

Hints

Step-by-step solution

Revise the chapter

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