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(D) In the given data,the highest frequency is $41,$ which corresponds to the modal class interval $10000-15000$.Here,the lower limit of the modal cla

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$11875$

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(D) In the given data,the highest frequency is $41,$ which corresponds to the modal class interval $10000-15000$.Here,the lower limit of the modal class $l = 10000$,the frequency of the modal class $f_m = 41$,the frequency of the class preceding the modal class $f_1 = 26$,the frequency of the class succeeding the modal class $f_2 = 16$,and the class size $h = 5000$.The formula for the mode is:$	ext{Mode} = l + \left( \frac{f_m - f_1}{2f_m - f_1 - f_2} ight) 	imes h$Substituting the values:$	ext{Mode} = 10000 + \left( \frac{41 - 26}{2 	imes 41 - 26 - 16} ight) 	imes 5000$$= 10000 + \left( \frac{15}{82 - 42} ight) 	imes 5000$$= 10000 + \left( \frac{15}{40} ight) 	imes 5000$$= 10000 + 15 	imes 125$$= 10000 + 1875 = 11875$Thus,the modal income is $Rs. 11875$.

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

Marks	$0-10$	$10-20$	$20-30$	$30-40$	$40-50$
No. of students	$20$	$10$	$20$	$30$	$20$

Class	$0-10$	$10-20$	$20-30$	$30-40$	$40-50$	$50-60$	$60-70$	$70-80$
Frequency	$2$	$6$	$8$	$x$	$20$	$18$	$y$	$14$

Class	$0-10$	$10-20$	$20-30$	$30-40$	$40-50$	$50-60$
Frequency	$7$	$12$	$x$	$28$	$y$	$9$

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 $Rs.$).

Similar Questions

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The median of the following frequency distribution is $49$ and the total frequency is $100$. Find the missing frequencies $x$ and $y$.

Class $0-10$ $10-20$ $20-30$ $30-40$ $40-50$ $50-60$ $60-70$ $70-80$

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The mode of the following data is $33 \frac{1}{3}$ and the total frequency is $100$. Find the missing frequencies $x$ and $y$.

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Frequency $7$ $12$ $x$ $28$ $y$ $9$

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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 $Rs.$).