The following table gives the distribution of the life time of 400 neon lamps: Life time (in hours) Number of lamps --- --- 1500-2000 14 2000-2500 56 2500-3000 60 3000-3500 86 3500-4000 74 4000-4500 62 4500-5000 48 Find the average life time of a lamp.

MathsCBSE Class 10 · Basic · Sample paper, session 2023-24 · 5 marks · Long answer

CBSE Class 10 Mathematics Basic sample paper 2023-24: question 35

From the official CBSE sample question paper for 2023-24, section D, question 35, for 5 marks. Try it first; the hints and our step-by-step solution are below.

Q35 · 5 marks · Long answerCompetency-basedStatistics

The following table gives the distribution of the life time of 400 neon lamps:

Life time (in hours)	Number of lamps
1500-2000	14
2000-2500	56
2500-3000	60
3000-3500	86
3500-4000	74
4000-4500	62
4500-5000	48

Find the average life time of a lamp.

Source: official sample paper from cbseacademic.nic.in (PDF). See it in the full Sample paper 2023-24.

Hints

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

Hint 1

Find the class marks and choose a middle one, such as 3250, as the assumed mean.

Hint 2

Compute $d = x - a$ and $f d$ for each class, then use $\overset{x}{ˉ} = a + \frac{Σ f d}{Σ f}$ .

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 $a = 3250$ and $d = x - a$ .

Life time (h)	$f$	$x$	$d$	$f d$
1500-2000	14	1750	−1500	−21000
2000-2500	56	2250	−1000	−56000
2500-3000	60	2750	−500	−30000
3000-3500	86	3250	0	0
3500-4000	74	3750	500	37000
4000-4500	62	4250	1000	62000
4500-5000	48	4750	1500	72000
Total	$Σ f = 400$			$Σ f d = 64000$

2 marks

Mean $\overset{x}{ˉ} = a + \frac{Σ f d}{Σ f}$
½ mark
$a = 3250$
½ mark
$\overset{x}{ˉ} = 3250 + \frac{64000}{400} = 3250 + 160$
1 mark
$\overset{x}{ˉ} = 3410$ . The average life time of a lamp is 3410 hours.
1 mark

Answer: Average life time = 3410 hours

Where the marks are

Correct table with class marks, $d$ and $f d$ , and totals $Σ f = 400$ , $Σ f d = 64000$ (2 marks)
Writes the assumed-mean formula (1/2 mark)
Chooses $a = 3250$ (1/2 mark)
Correct substitution (1 mark)
Mean = 3410 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 paperSample paper 2023-24 (Basic): every question, by section.

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CBSE Class 10 Mathematics Basic sample paper 2023-24: question 35

Hints

Step-by-step solution

Revise the chapter

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