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(D) The cumulative frequencies with their respective class intervals are as follows:Life timeNumber of lamps $(f_i)$Cumulative frequency $(cf)$$1500-2

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$3406.98$

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(D) The cumulative frequencies with their respective class intervals are as follows:Life timeNumber of lamps $(f_i)$Cumulative frequency $(cf)$$1500-2000$$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$$400$Here,$n = 400$,so $\frac{n}{2} = 200$.The cumulative frequency just greater than $200$ is $216$,which corresponds to the class interval $3000-3500$.Thus,the median class is $3000-3500$.Lower limit $(l)$ of the median class = $3000$.Frequency $(f)$ of the median class = $86$.Cumulative frequency $(cf)$ of the class preceding the median class = $130$.Class size $(h)$ = $500$.Using the median formula: $	ext{Median} = l + \left( \frac{\frac{n}{2} - cf}{f} ight) 	imes h$$	ext{Median} = 3000 + \left( \frac{200 - 130}{86} ight) 	imes 500$$	ext{Median} = 3000 + \left( \frac{70}{86} ight) 	imes 500$$	ext{Median} = 3000 + \frac{35000}{86} \approx 3000 + 406.98 = 3406.98$.Therefore,the median lifetime of a lamp is $3406.98 	ext{ hours}$.

Weekly income	Number of families
$0-1000$	$250$
$1000-2000$	$190$
$2000-3000$	$100$
$3000-4000$	$40$
$4000-5000$	$15$
$5000-6000$	$5$
Total	$600$

Class	$20-25$	$25-30$	$30-35$	$35-40$	$40-45$	$45-50$	$50-55$
Frequency	$2$	$5$	$8$	$10$	$7$	$10$	$3$

Class	$0-100$	$100-200$	$200-300$	$300-400$	$400-500$	$500-600$	$600-700$	$700-800$	$800-900$	$900-1000$
Frequency	$2$	$5$	$x$	$12$	$17$	$20$	$y$	$9$	$7$	$4$

Weight (in kg)	Number of students
Less than $38$	$0$
Less than $40$	$3$
Less than $42$	$5$
Less than $44$	$9$
Less than $46$	$14$
Less than $48$	$28$
Less than $50$	$32$
Less than $52$	$35$

The following table gives the distribution of the lifetime 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 lifetime of a lamp.

Similar Questions

Weekly income of $600$ families is tabulated below:

Weekly income Number of families

$0-1000$ $250$

$1000-2000$ $190$

$2000-3000$ $100$

$3000-4000$ $40$

$4000-5000$ $15$

$5000-6000$ $5$

Total $600$

Compute the median income (in $Rs.$).

The abscissa of the point of intersection of the less than type and of the more than type cumulative frequency curves of a grouped data gives its

The median class in the following frequency distribution is ..........

Class $20-25$ $25-30$ $30-35$ $35-40$ $40-45$ $45-50$ $50-55$

Frequency $2$ $5$ $8$ $10$ $7$ $10$ $3$

The median of the following frequency distribution is $525$ and the total frequency is $100$. Find the missing frequencies $x$ and $y$.

Class $0-100$ $100-200$ $200-300$ $300-400$ $400-500$ $500-600$ $600-700$ $700-800$ $800-900$ $900-1000$

Frequency $2$ $5$ $x$ $12$ $17$ $20$ $y$ $9$ $7$ $4$

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

The following table gives the distribution of the lifetime 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 lifetime of a lamp.