Find the median of the following frequency di | vedclass

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(A) To find the median,we first calculate the cumulative frequency $(cf)$:| Class | Frequency $(f)$ | Cumulative Frequency $(cf)$ || :--- | :--- | :--

Vedclass · Accepted Answer

$153.79$

Vedclass · Answer

(A) To find the median,we first calculate the cumulative frequency $(cf)$:| Class | Frequency $(f)$ | Cumulative Frequency $(cf)$ || :--- | :--- | :--- || $110-120$ | $6$ | $6$ || $120-130$ | $25$ | $31$ || $130-140$ | $48$ | $79$ || $140-150$ | $72$ | $151$ || $150-160$ | $116$ | $267$ || $160-170$ | $60$ | $327$ || $170-180$ | $38$ | $365$ || $180-190$ | $22$ | $387$ || $190-200$ | $3$ | $390$ |Total frequency $N = 390$. So,$N/2 = 390/2 = 195$.The cumulative frequency just greater than $195$ is $267$,which corresponds to the class interval $150-160$.Thus,the median class is $150-160$.Here,lower limit $l = 150$,frequency of median class $f = 116$,cumulative frequency of the class preceding the median class $cf = 151$,and class size $h = 10$.Using the median formula: $	ext{Median} = l + \left( \frac{N/2 - cf}{f} ight) 	imes h$$	ext{Median} = 150 + \left( \frac{195 - 151}{116} ight) 	imes 10$$	ext{Median} = 150 + \left( \frac{44}{116} ight) 	imes 10 = 150 + \frac{440}{116} \approx 150 + 3.79 = 153.79$.

Marks (out of $90$)	Number of candidates
More than or equal to $80$	$4$
More than or equal to $70$	$6$
More than or equal to $60$	$11$
More than or equal to $50$	$17$
More than or equal to $40$	$23$
More than or equal to $30$	$27$
More than or equal to $20$	$30$
More than or equal to $10$	$32$
More than or equal to $0$	$34$

Class	$4-7$	$8-11$	$12-15$	$16-19$
Frequency	$5$	$4$	$9$	$10$

Income (in $Rs.$)	Number of families
$0-5000$	$8$
$5000-10000$	$26$
$10000-15000$	$41$
$15000-20000$	$16$
$20000-25000$	$3$
$25000-30000$	$3$
$30000-35000$	$2$
$35000-40000$	$1$

Find the median of the following frequency distribution:

Class Frequency $(f)$

$110-120$ $6$

$120-130$ $25$

$130-140$ $48$

$140-150$ $72$

$150-160$ $116$

$160-170$ $60$

$170-180$ $38$

$180-190$ $22$

$190-200$ $3$

Similar Questions

For a given frequency distribution,the frequencies of the first,second,and third class are $8$,$15$,and $18$ respectively. Then,the cumulative frequency of the third class is $\ldots \ldots \ldots \ldots .$

Calculate the mean of the following data:

Class $4-7$ $8-11$ $12-15$ $16-19$

Frequency $5$ $4$ $9$ $10$

The monthly income of $100$ families is given as follows:

Income (in $Rs.$) Number of families

$0-5000$ $8$

$5000-10000$ $26$

$10000-15000$ $41$

$15000-20000$ $16$

$20000-25000$ $3$

$25000-30000$ $3$

$30000-35000$ $2$

$35000-40000$ $1$

Calculate the modal income (in $Rs.$).

For a given frequency distribution,$A=49.5, \Sigma f_{i}=40, \Sigma f_{i} u_{i}=-5$ and $c=20$. Then,mean $\bar{x}=$ ............

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Class	Frequency $(f)$
$110-120$	$6$
$120-130$	$25$
$130-140$	$48$
$140-150$	$72$
$150-160$	$116$
$160-170$	$60$
$170-180$	$38$
$180-190$	$22$
$190-200$	$3$

Find the median of the following frequency distribution: Class Frequency $(f)$ $110-120$ $6$ $120-130$ $25$ $130-140$ $48$ $140-150$ $72$ $150-160$ $116$ $160-170$ $60$ $170-180$ $38$ $180-190$ $22$ $190-200$ $3$