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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}}{

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$145.20$

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(A) To find the class mark $(x_i)$ for each interval,the following relation is used:$x_i = \frac{	ext{Upper class limit} + 	ext{Lower class limit}}{2}$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 $Rs. 145.20$.

Percentage of female teachers	$15$-$25$	$25$-$35$	$35$-$45$	$45$-$55$	$55$-$65$	$65$-$75$	$75$-$85$
Number of States/$U$.$T$.	$6$	$11$	$7$	$4$	$4$	$2$	$1$

Daily pocket allowance (in $Rs.$)	$11-13$	$13-15$	$15-17$	$17-19$	$19-21$	$21-23$	$23-25$
Number of children	$7$	$6$	$9$	$13$	$f$	$5$	$4$

Class interval	Frequency
$0-100$	$2$
$100-200$	$5$
$200-300$	$x$
$300-400$	$12$
$400-500$	$17$
$500-600$	$20$
$600-700$	$y$
$700-800$	$9$
$800-900$	$7$
$900-1000$	$4$

Life time (in hours)	Number of lamps
$1500-2000$	$14$
$2000-2500$	$56$
$2500-3000$	$60$
$3000-3500$	$86$
$3500-4000$	$74$
$4000-4500$	$62$
$4500-5000$	$48$

Lifetimes (in hours)	$0-20$	$20-40$	$40-60$	$60-80$	$80-100$	$100-120$
Frequency	$10$	$35$	$52$	$61$	$38$	$29$

Similar Questions

The following distribution shows the daily pocket allowance of children of a locality. The mean pocket allowance is $Rs. 18$. Find the missing frequency $f$.
Daily pocket allowance (in $Rs.$) $11-13$ $13-15$ $15-17$ $17-19$ $19-21$ $21-23$ $23-25$
Number of children $7$ $6$ $9$ $13$ $f$ $5$ $4$

The median of the following data is $525$. Find the values of $x$ and $y$,if the total frequency is $100$.
Class interval Frequency
$0-100$ $2$
$100-200$ $5$
$200-300$ $x$
$300-400$ $12$
$400-500$ $17$
$500-600$ $20$
$600-700$ $y$
$700-800$ $9$
$800-900$ $7$
$900-1000$ $4$

The following table gives the distribution of the lifetime of $400$ neon lamps:
Life time (in hours) Number of lamps
$1500-2000$ $14$
$2000-2500$ $56$
$2500-3000$ $60$
$3000-3500$ $86$
$3500-4000$ $74$
$4000-4500$ $62$
$4500-5000$ $48$

Find the median lifetime of a lamp.

The following data provides information on the observed lifetimes (in $hours$) of $225$ electrical components:
Lifetimes (in hours) $0-20$ $20-40$ $40-60$ $60-80$ $80-100$ $100-120$
Frequency $10$ $35$ $52$ $61$ $38$ $29$

Determine the modal lifetimes of the components.

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The following distribution shows the daily pocket allowance of children of a locality. The mean pocket allowance is $Rs. 18$. Find the missing frequency $f$.Daily pocket allowance (in $Rs.$)$11-13$$13-15$$15-17$$17-19$$19-21$$21-23$$23-25$Number of children$7$$6$$9$$13$$f$$5$$4$

The median of the following data is $525$. Find the values of $x$ and $y$,if the total frequency is $100$.Class intervalFrequency$0-100$$2$$100-200$$5$$200-300$$x$$300-400$$12$$400-500$$17$$500-600$$20$$600-700$$y$$700-800$$9$$800-900$$7$$900-1000$$4$

The following table gives the distribution of the lifetime of $400$ neon lamps:Life time (in hours)Number of lamps$1500-2000$$14$$2000-2500$$56$$2500-3000$$60$$3000-3500$$86$$3500-4000$$74$$4000-4500$$62$$4500-5000$$48$Find the median lifetime of a lamp.

The following data provides information on the observed lifetimes (in $hours$) of $225$ electrical components:Lifetimes (in hours)$0-20$$20-40$$40-60$$60-80$$80-100$$100-120$Frequency$10$$35$$52$$61$$38$$29$Determine the modal lifetimes of the components.