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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
$0-5000$	$8$
$5000-10000$	$26$
$10000-15000$	$41$
$15000-20000$	$16$
$20000-25000$	$3$
$25000-30000$	$3$
$30000-35000$	$2$
$35000-40000$	$1$

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

Marks (out of $90$)	Number of candidates
More than or equal to $80$	$4$
More than or equal to $70$	$6$
More than or equal to $60$	$11$
More than or equal to $50$	$17$
More than or equal to $40$	$23$
More than or equal to $30$	$27$
More than or equal to $20$	$30$
More than or equal to $10$	$32$
More than or equal to $0$	$34$

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

Find the median of the following frequency distribution:

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

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

For a given frequency distribution,$\bar{x}=20, \Sigma f_{i} u_{i}=-50, n=100$ and $c=10$. Then,assumed mean $A = \ldots \ldots \ldots \ldots$

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

If $Z+M=88$ and $Z-M=2$,then $M=\ldots \ldots \ldots \ldots . .$

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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 $Rs.$).