Find the median of the following frequency di | vedclass

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(C) To find the median,we first calculate the cumulative frequency $(cf)$:  ClassFrequency $(f)$Cumulative Frequency $(cf)$  $30-35$$1$$1$  $35-40$$2$

Vedclass · Accepted Answer

$54.56$

Vedclass · Answer

(C) To find the median,we first calculate the cumulative frequency $(cf)$:  ClassFrequency $(f)$Cumulative Frequency $(cf)$  $30-35$$1$$1$  $35-40$$2$$3$  $40-45$$5$$8$  $45-50$$10$$18$  $50-55$$17$$35$  $55-60$$15$$50$  $60-65$$9$$59$  $65-70$$5$$64$  $70-75$$3$$67$Total frequency $N = 67$. So,$N/2 = 67/2 = 33.5$.Looking at the $cf$ column,the median class is $50-55$ because $33.5$ lies in this interval.Here,lower limit $l = 50$,class size $h = 5$,frequency of median class $f = 17$,and cumulative frequency of the class preceding the median class $cf = 18$.Using the median formula: $	ext{Median} = l + \left( \frac{N/2 - cf}{f} ight) 	imes h$$	ext{Median} = 50 + \left( \frac{33.5 - 18}{17} ight) 	imes 5$$	ext{Median} = 50 + \left( \frac{15.5}{17} ight) 	imes 5$$	ext{Median} = 50 + \frac{77.5}{17} \approx 50 + 4.5588 \approx 54.56$.

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

Class	$0-10$	$10-20$	$20-30$	$30-40$	$40-50$	$50-60$
Frequency	$4$	$5$	$9$	$10$	$14$	$8$

Monthly income range (in $Rs.$)	Number of families
Income more than $10000$	$100$
Income more than $13000$	$85$
Income more than $16000$	$69$
Income more than $19000$	$50$
Income more than $22000$	$33$
Income more than $25000$	$15$

Find the median of the following frequency distribution:

Class $30-35$ $35-40$ $40-45$ $45-50$ $50-55$ $55-60$ $60-65$ $65-70$ $70-75$

Frequency $1$ $2$ $5$ $10$ $17$ $15$ $9$ $5$ $3$

Similar Questions

In the formula $M = l + \frac{(\frac{n}{2} - cf)}{f} \times c$ for the median,$cf = \ldots \ldots \ldots$

Find the median of the following frequency distribution:

Class Frequency $(f)$

$110-120$ $6$

$120-130$ $25$

$130-140$ $48$

$140-150$ $72$

$150-160$ $116$

$160-170$ $60$

$170-180$ $38$

$180-190$ $22$

$190-200$ $3$

The median class of the following frequency distribution is ...........
Class $0-10$ $10-20$ $20-30$ $30-40$ $40-50$ $50-60$
Frequency $4$ $5$ $9$ $10$ $14$ $8$

Total frequency $n = 50$.

In the formula $M = l + \frac{(\frac{n}{2} - cf)}{f} \times h$ for the median,$l = \ldots \ldots \ldots$

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Find the median of the following frequency distribution: Class $30-35$ $35-40$ $40-45$ $45-50$ $50-55$ $55-60$ $60-65$ $65-70$ $70-75$ Frequency $1$ $2$ $5$ $10$ $17$ $15$ $9$ $5$ $3$