The following table gives the distribution of the life time of 400 neon lamps-Whinein hours - Whline 1500-2000 - 14 Whline2000-2500 - 56 Whline2500-3000 - 60 Wlline3000-3500 - 86 Wllhline3500-4000 - 74 Wllhline4000-4500 - 62 Whline 4500-5000 - 48 Whhine e n d array Find the median life time of a lamp- -4 MARKS-

Concept: 1 Mark Application: 3 Marks [ Life time amp; Number of amp; Cumulative; (in hours) ...

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Standard IX

Mathematics

Class Interval

The following...

Question

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

$\begin{matrix} Life time & Number of lamps (in hours) 1500 - 2000 & 14 2000 - 2500 & 56 2500 - 3000 & 60 3000 - 3500 & 86 3500 - 4000 & 74 4000 - 4500 & 62 4500 - 5000 & 48 \end{matrix}$

Find the median life time of a lamp. [4 MARKS]

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Solution

Concept: 1 Mark
Application: 3 Marks

$\begin{matrix} Life time & Number of & Cumulative (in hours) & lamps & Frequency 1500 - 2000 & 14 & 14 2000 - 2500 & 56 & 70 2500 - 3000 & 60 & 130 3000 - 3500 & 86 & 216 3500 - 4000 & 74 & 290 4000 - 4500 & 62 & 352 4500 - 5000 & 48 & 400 \end{matrix}$

Now, n= 400

So, $\frac{n}{2} = \frac{400}{2} = 200$

This observation lies in the class 3000-3500

So, 3000-3500 is the median class

Therefore, l = 3000, h = 500, cf = 130, f = 86

$∴ M e d i a n = l + (\frac{\frac{n}{2} - c f}{f}) \times h = 3000 + (\frac{200 - 130}{86}) \times 500$

$= 3000 + 406.98 = 3406.98 h o u r s$

Hence, the median life time of a lamp is 3406.98 hours

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

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

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Question 5
The following table gives the distribution of the life time of 400 neon lamps:

$\begin{matrix} L i f e t i m e (i n h o u r s) & N u m b e r o f l a m p s 1500 - 2000 & 14 2000 - 2500 & 56 2500 - 3000 & 60 3000 - 3500 & 86 3500 - 4000 & 74 4000 - 4500 & 62 4500 - 5000 & 48 \end{matrix}$

Find the median life time of a lamp.

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

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

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The following table gives the distribution of the life time of 400 neon lamps:
$\begin{matrix} Lite time : (in hours) & Number of lamps 1500 - 2000 & 14 2000 - 2500 & 56 2500 - 3000 & 60 3000 - 3500 & 86 3500 - 4000 & 74 4000 - 4500 & 62 4500 - 5000 & 48 \end{matrix}$
Find the median life.

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The following table gives the distribution of the life time of 400 neon lamps: Life timeNumber of lamps(in hours) 1500−2000142000−2500562500−3000603000−3500863500−4000744000−4500624500−500048 Find the median life time of a lamp. [4 MARKS]