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(A) To find the class mark $(x_i)$ for each interval,the following relation is used:$x_i = \frac{	ext{Upper class limit} + 	ext{Lower class limit}}{

Vedclass · Accepted Answer

$145.20$

Vedclass · Answer

(A) To find the class mark $(x_i)$ for each interval,the following relation is used:$x_i = \frac{	ext{Upper class limit} + 	ext{Lower class limit}}{2}$Class size $(h)$ of this data $= 20$.Taking $150$ as the assumed mean $(a)$,$d_i$,$u_i$,and $f_i u_i$ can be calculated as follows:$\begin{array}{|c|c|c|c|c|c|} \hline 	ext{Daily wages} & f_i & x_i & d_i = x_i - 150 & u_i = \frac{d_i}{20} & f_i u_i \ \hline 100-120 & 12 & 110 & -40 & -2 & -24 \ \hline 120-140 & 14 & 130 & -20 & -1 & -14 \ \hline 140-160 & 8 & 150 & 0 & 0 & 0 \ \hline 160-180 & 6 & 170 & 20 & 1 & 6 \ \hline 180-200 & 10 & 190 & 40 & 2 & 20 \ \hline 	ext{Total} & 50 & & & & -12 \ \hline \end{array}$From the table,we have:$\sum f_i = 50$$\sum f_i u_i = -12$Using the step-deviation method,the mean $\bar{x}$ is given by:$\bar{x} = a + \left( \frac{\sum f_i u_i}{\sum f_i} ight) 	imes h$$\bar{x} = 150 + \left( \frac{-12}{50} ight) 	imes 20$$\bar{x} = 150 - \frac{240}{50} = 150 - 4.8$$\bar{x} = 145.2$Therefore,the mean daily wage of the workers is $Rs. 145.20$.

Age (in years)	Number of policy holders
Below $20$	$2$
Below $25$	$6$
Below $30$	$24$
Below $35$	$45$
Below $40$	$78$
Below $45$	$89$
Below $50$	$92$
Below $55$	$98$
Below $60$	$100$

Weight (in kg)	Number of students
Less than $38$	$0$
Less than $40$	$3$
Less than $42$	$5$
Less than $44$	$9$
Less than $46$	$14$
Less than $48$	$28$
Less than $50$	$32$
Less than $52$	$35$

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

Runs scored	Number of batsmen
$3000-4000$	$4$
$4000-5000$	$18$
$5000-6000$	$9$
$6000-7000$	$7$
$7000-8000$	$6$
$8000-9000$	$3$
$9000-10000$	$1$
$10000-11000$	$1$

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

Similar Questions

The distribution below gives the weights of $30$ students of a class. Find the median weight of the students.
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Number of students $2$ $3$ $8$ $6$ $6$ $3$ $2$

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