The distribution below gives the weights of 3 | vedclass

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Question

(C) The cumulative frequencies with their respective class intervals are as follows:Weight (in kg)Frequency $(f_i)$Cumulative frequency $(cf)$$40-45$$

Vedclass · Accepted Answer

$56.67$

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(C) The cumulative frequencies with their respective class intervals are as follows:Weight (in kg)Frequency $(f_i)$Cumulative frequency $(cf)$$40-45$$2$$2$$45-50$$3$$5$$50-55$$8$$13$$55-60$$6$$19$$60-65$$6$$25$$65-70$$3$$28$$70-75$$2$$30$Total number of students $n = 30$.We calculate $\frac{n}{2} = \frac{30}{2} = 15$.The cumulative frequency just greater than $15$ is $19$,which corresponds to the class interval $55-60$.Thus,the median class is $55-60$.Lower limit of the median class $(l)$ = $55$.Frequency of the median class $(f)$ = $6$.Cumulative frequency of the class preceding the median class $(cf)$ = $13$.Class size $(h)$ = $5$.Using the median formula: $	ext{Median} = l + \left( \frac{\frac{n}{2} - cf}{f} ight) 	imes h$.$	ext{Median} = 55 + \left( \frac{15 - 13}{6} ight) 	imes 5$.$	ext{Median} = 55 + \left( \frac{2}{6} ight) 	imes 5 = 55 + \frac{10}{6} = 55 + 1.67 = 56.67$.Therefore,the median weight of the students is $56.67 	ext{ kg}$.

Class	$0-5$	$6-11$	$12-17$	$18-23$	$24-29$
Frequency	$13$	$10$	$15$	$8$	$11$

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

Class	$65-85$	$85-105$	$105-125$	$125-145$	$145-165$	$165-185$	$185-205$
Frequency	$4$	$5$	$13$	$20$	$14$	$8$	$4$

Class	$10-20$	$20-30$	$30-40$	$40-50$	$50-60$	$60-70$	$70-80$
Frequency	$6$	$10$	$5$	$6$	$4$	$2$	$2$

Class	$12.5-17.5$	$17.5-22.5$	$22.5-27.5$	$27.5-32.5$	$32.5-37.5$
Frequency	$2$	$22$	$19$	$14$	$13$

The distribution below gives the weights of $30$ students of a class. Find the median weight of the students.
Weight (in kg) $40-45$ $45-50$ $50-55$ $55-60$ $60-65$ $65-70$ $70-75$
Number of students $2$ $3$ $8$ $6$ $6$ $3$ $2$

Similar Questions

Consider the following frequency distribution:

Class $0-5$ $6-11$ $12-17$ $18-23$ $24-29$

Frequency $13$ $10$ $15$ $8$ $11$

The upper limit of the median class is

Find the median of the following frequency distribution:

Class $65-85$ $85-105$ $105-125$ $125-145$ $145-165$ $165-185$ $185-205$

Frequency $4$ $5$ $13$ $20$ $14$ $8$ $4$

The median class of the following frequency distribution is ...........
Class $10-20$ $20-30$ $30-40$ $40-50$ $50-60$ $60-70$ $70-80$
Frequency $6$ $10$ $5$ $6$ $4$ $2$ $2$

Construct the cumulative frequency distribution of the following distribution:

Class $12.5-17.5$ $17.5-22.5$ $22.5-27.5$ $27.5-32.5$ $32.5-37.5$

Frequency $2$ $22$ $19$ $14$ $13$

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Weight (in kg)	$40-45$	$45-50$	$50-55$	$55-60$	$60-65$	$65-70$	$70-75$
Number of students	$2$	$3$	$8$	$6$	$6$	$3$	$2$

The distribution below gives the weights of $30$ students of a class. Find the median weight of the students.Weight (in kg)$40-45$$45-50$$50-55$$55-60$$60-65$$65-70$$70-75$Number of students$2$$3$$8$$6$$6$$3$$2$

Similar Questions

Consider the following frequency distribution: Class $0-5$ $6-11$ $12-17$ $18-23$ $24-29$ Frequency $13$ $10$ $15$ $8$ $11$ The upper limit of the median class is

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.

Find the median of the following frequency distribution: Class $65-85$ $85-105$ $105-125$ $125-145$ $145-165$ $165-185$ $185-205$ Frequency $4$ $5$ $13$ $20$ $14$ $8$ $4$

The median class of the following frequency distribution is ...........Class$10-20$$20-30$$30-40$$40-50$$50-60$$60-70$$70-80$Frequency$6$$10$$5$$6$$4$$2$$2$

Construct the cumulative frequency distribution of the following distribution: Class $12.5-17.5$ $17.5-22.5$ $22.5-27.5$ $27.5-32.5$ $32.5-37.5$ Frequency $2$ $22$ $19$ $14$ $13$