The frequency distribution of the daily house | vedclass

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(D) The mode of the distribution is given as $140$. Since $140$ lies in the class interval $100-150$,the modal class is $100-150$.
The formula for mo

Vedclass · Accepted Answer

$36$

Vedclass · Answer

(D) The mode of the distribution is given as $140$. Since $140$ lies in the class interval $100-150$,the modal class is $100-150$.
The formula for mode is $Z = l + \left( \frac{f_1 - f_0}{2f_1 - f_0 - f_2} ight) 	imes h$.
Here,$l = 100$ (lower limit of modal class),$f_1 = 37$ (frequency of modal class),$f_0 = 33$ (frequency of preceding class),$f_2 = b$ (frequency of succeeding class),and $h = 50$ (class size).
Substituting the values:
$140 = 100 + \left( \frac{37 - 33}{2(37) - 33 - b} ight) 	imes 50$
$40 = \left( \frac{4}{74 - 33 - b} ight) 	imes 50$
$40 = \frac{200}{41 - b}$
$40(41 - b) = 200$
$41 - b = 5$
$b = 41 - 5 = 36$.
Thus,the value of $b$ is $36$.

Daily Expenditure (	$0-50$	$50-100$	$100-150$	$150-200$	$200-250$
Number of Families $(f)$	$24$	$33$	$37$	$b$	$25$

Items of expenditure	Number of families
$Education$	$150$
$Food and clothing$	$400$
$House rent$	$40$
$Electricity$	$250$
$Miscellaneous$	$160$

The frequency distribution of the daily household expenditure of some families in a residential area is given below. If the mode of the distribution is $140$,what is the value of $b$?

Daily Expenditure ( $0-50$ $50-100$ $100-150$ $150-200$ $200-250$

Number of Families $(f)$ $24$ $33$ $37$ $b$ $25$

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$Education$ $150$

$Food and clothing$ $400$

$House rent$ $40$

$Electricity$ $250$

$Miscellaneous$ $160$

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The frequency distribution of the daily household expenditure of some families in a residential area is given below. If the mode of the distribution is $140$,what is the value of $b$? Daily Expenditure ( $0-50$ $50-100$ $100-150$ $150-200$ $200-250$ Number of Families $(f)$ $24$ $33$ $37$ $b$ $25$