A survey conducted on 20 households in a loca | vedclass

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(B) Here,the maximum class frequency is $8$,and the class corresponding to this frequency is $3-5$.So,the modal class is $3-5$.Now,Modal class $= 3-5$

Vedclass · Accepted Answer

$3.286$

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(B) Here,the maximum class frequency is $8$,and the class corresponding to this frequency is $3-5$.So,the modal class is $3-5$.Now,Modal class $= 3-5$,lower limit $(l)$ of modal class $= 3$,class size $(h) = 2$.Frequency $(f_1)$ of the modal class $= 8$.Frequency $(f_0)$ of the class preceding the modal class $= 7$.Frequency $(f_2)$ of the class succeeding the modal class $= 2$.Now,let us substitute these values in the formula:Mode $= l + \left( \frac{f_1 - f_0}{2f_1 - f_0 - f_2} ight) 	imes h$Mode $= 3 + \left( \frac{8 - 7}{2 	imes 8 - 7 - 2} ight) 	imes 2 = 3 + \frac{2}{7} = 3 + 0.286 = 3.286$.Therefore,the mode of the data above is $3.286$.

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

Class interval	Frequency
$0-10$	$5$
$10-20$	$x$
$20-30$	$20$
$30-40$	$15$
$40-50$	$y$
$50-60$	$5$
Total	$60$

Height (in $cm$)	Number of girls
Less than $140$	$4$
Less than $145$	$11$
Less than $150$	$29$
Less than $155$	$40$
Less than $160$	$46$
Less than $165$	$51$

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

Marks obtained $(x_{i})$	$10, 20, 36, 40, 50, 56, 60, 70, 72, 80, 88, 92, 95$
Number of students $(f_{i})$	$1, 1, 3, 4, 3, 2, 4, 4, 1, 1, 2, 3, 1$

$A$ 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.

Similar Questions

If the median of the distribution given below is $28.5,$ find the values of $x$ and $y$.
Class interval Frequency
$0-10$ $5$
$10-20$ $x$
$20-30$ $20$
$30-40$ $15$
$40-50$ $y$
$50-60$ $5$
Total $60$

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 $2$ $3$ $8$ $6$ $6$ $3$ $2$

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Monthly consumption (in units)	Number of consumers
$65-85$	$4$
$85-105$	$5$
$105-125$	$13$
$125-145$	$20$
$145-165$	$14$
$165-185$	$8$
$185-205$	$4$

$A$ 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.