A life insurance agent found the following da | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) The given data is in the form of 'less than' cumulative frequency distribution. We first convert it into class intervals with their respective fre

Vedclass · Accepted Answer

$35.76$

Vedclass · Answer

(B) The given data is in the form of 'less than' cumulative frequency distribution. We first convert it into class intervals with their respective frequencies.Age (in years)Frequency $(f_i)$Cumulative frequency $(cf)$$18-20$$2$$2$$20-25$$6-2=4$$6$$25-30$$24-6=18$$24$$30-35$$45-24=21$$45$$35-40$$78-45=33$$78$$40-45$$89-78=11$$89$$45-50$$92-89=3$$92$$50-55$$98-92=6$$98$$55-60$$100-98=2$$100$Here,$n = 100$,so $\frac{n}{2} = 50$.The cumulative frequency just greater than $50$ is $78$,which corresponds to the class interval $35-40$.Thus,the median class is $35-40$.Lower limit $(l)$ $= 35$,class size $(h)$ $= 5$,frequency of median class $(f)$ $= 33$,and cumulative frequency of the class preceding the median class $(cf)$ $= 45$.Using the median formula: $	ext{Median} = l + \left( \frac{\frac{n}{2} - cf}{f} ight) 	imes h$$	ext{Median} = 35 + \left( \frac{50 - 45}{33} ight) 	imes 5$$	ext{Median} = 35 + \left( \frac{5}{33} ight) 	imes 5 = 35 + \frac{25}{33} \approx 35 + 0.76 = 35.76$.Therefore,the median age is $35.76$ years.

Daily income (in Rs.)	$100-120$	$120-140$	$140-160$	$160-180$	$180-200$
Number of workers	$12$	$14$	$8$	$6$	$10$

Age (in years)	$5$-$15$	$15$-$25$	$25$-$35$	$35$-$45$	$45$-$55$	$55$-$65$
Number of patients	$6$	$11$	$21$	$23$	$14$	$5$

Length (in mm)	Number of leaves
$118-126$	$3$
$127-135$	$5$
$136-144$	$9$
$145-153$	$12$
$154-162$	$5$
$163-171$	$4$
$172-180$	$2$

Family size	$1-3$	$3-5$	$5-7$	$7-9$	$9-11$
Number of families	$7$	$8$	$2$	$2$	$1$

Number of plants	$0-2$	$2-4$	$4-6$	$6-8$	$8-10$	$10-12$	$12-14$
Number of houses	$1$	$2$	$1$	$5$	$6$	$2$	$3$

Similar Questions

The following distribution gives the daily income of $50$ workers of a factory.
Daily income (in Rs.) $100-120$ $120-140$ $140-160$ $160-180$ $180-200$
Number of workers $12$ $14$ $8$ $6$ $10$

Convert the distribution above to a less than type cumulative frequency distribution,and draw its ogive.

$A$ survey conducted on $20$ households in a locality by a group of students resulted in the following frequency table for the number of family members in a household:
Family size $1-3$ $3-5$ $5-7$ $7-9$ $9-11$
Number of families $7$ $8$ $2$ $2$ $1$

Find the mode of this data.

Vedclass Test Series

Exam Paper Generator

Online Exam Module

Age (in years)	Number of policy holders
Below $20$	$2$
Below $25$	$6$
Below $30$	$24$
Below $35$	$45$
Below $40$	$78$
Below $45$	$89$
Below $50$	$92$
Below $55$	$98$
Below $60$	$100$

Similar Questions

The following distribution gives the daily income of $50$ workers of a factory.Daily income (in Rs.)$100-120$$120-140$$140-160$$160-180$$180-200$Number of workers$12$$14$$8$$6$$10$Convert the distribution above to a less than type cumulative frequency distribution,and draw its ogive.

The lengths of $40$ leaves of a plant are measured correct to the nearest millimetre,and the data obtained is represented in the following table:Length (in mm)Number of leaves$118-126$$3$$127-135$$5$$136-144$$9$$145-153$$12$$154-162$$5$$163-171$$4$$172-180$$2$Find the median length of the leaves.

$A$ survey conducted on $20$ households in a locality by a group of students resulted in the following frequency table for the number of family members in a household:Family size$1-3$$3-5$$5-7$$7-9$$9-11$Number of families$7$$8$$2$$2$$1$Find the mode of this data.

Vedclass Test Series

Exam Paper Generator

Online Exam Module

The following distribution gives the daily income of $50$ workers of a factory.
Daily income (in Rs.) $100-120$ $120-140$ $140-160$ $160-180$ $180-200$
Number of workers $12$ $14$ $8$ $6$ $10$

Convert the distribution above to a less than type cumulative frequency distribution,and draw its ogive.

$A$ survey conducted on $20$ households in a locality by a group of students resulted in the following frequency table for the number of family members in a household:
Family size $1-3$ $3-5$ $5-7$ $7-9$ $9-11$
Number of families $7$ $8$ $2$ $2$ $1$

Find the mode of this data.