Question 5 The following table gives the distribution of the life time of 400 neon lamps- beginarray -c- c - hline Life time in hours-Number of lampsiWhline 1500-2000-14-Whline2000-2500-56Whline 2500-3000-60Whline 3000-3500-86Whline 3500-4000 - 74 Whline 4000-4500-62 Whline4500-5000-48Whline end array Find the median life time of a lamp-

Name: NCERT - Grade 10 - Mathematics - Statistics - Q20
Uploaded: 2022-07-04T10:36:42+05:30
Description: We can find the cumulative frequencies with their respective class intervals as below: [ Life time amp;Number of lamps (f_i) amp;Cumulative fre ...

We can find the cumulative frequencies with their respective class intervals as below: [ Life time amp;Number of lamps (f_i) amp;Cumulative fre ...

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Standard X

Mathematics

Cumulative Frequency Distribution of Less Than Type

Question 5 Th...

Question

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.

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Solution

We can find the cumulative frequencies with their respective class intervals as below:

$\begin{matrix} L i f e t i m e & N u m b e r o f l a m p s (f_{i}) & C u m u l a t i v e f r e q u e n c y 1500 - 2000 & 14 & 14 2000 - 2500 & 56 & 14 + 56 = 70 2500 - 3000 & 60 & 70 + 60 = 130 3000 - 3500 & 86 & 130 + 86 = 216 3500 - 4000 & 74 & 216 + 74 = 290 4000 - 4500 & 62 & 290 + 62 = 352 4500 - 5000 & 48 & 352 + 48 = 400 T o t a l (n) & 400 \end{matrix}$

Now, we may observe that cumulative frequency just greater than $\frac{n}{2} (i . e ., \frac{400}{2} = 200)$ is 216 belonging to class interval 3000 - 3500.

Median class = 3000 - 3500

Lower limit $l$ of median class = 3000

Frequency $f$ of median class = 86

Cumulative frequency $c_{f}$ of class preceding median class = 130 Class size $h$ = 500

$M e d i a n = l + (\frac{\frac{n}{2} - c_{f}}{f}) \times h = 3000 \times (\frac{200 - 130}{86}) \times 500 = 3000 + \frac{70 \times 500}{86} = 3000 + 406.98 = 3406.98$

So, median life time of lamps is 3406.98 hours.

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Similar questions

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

Find the median life.

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

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

Find the median life time of a lamp.

Q. 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 median life.

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.

Find 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 median life time of a lamp.

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Cumulative Frequency Distribution of Less Than Type

Standard X Mathematics

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Question 5 The following table gives the distribution of the life time of 400 neon lamps: Life time (in hours)Number of lamps1500−2000142000−2500562500−3000603000−3500863500−4000744000−4500624500−500048 Find the median life time of a lamp.