The daily income of a sample of 50 employees | vedclass

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(D) Since the given data is not continuous,we first convert it into continuous classes by subtracting $0.5$ from the lower limit and adding $0.5$ to t

Vedclass · Accepted Answer

$356$

Vedclass · Answer

(D) Since the given data is not continuous,we first convert it into continuous classes by subtracting $0.5$ from the lower limit and adding $0.5$ to the upper limit of each class.Now,we calculate the class mark $(x_i)$ for each class and use the step-deviation method:						Income (in $Rs.$)			Class mark $(x_i)$			Frequency $(f_i)$			$u_i = \frac{x_i - a}{h}$			$f_i u_i$							$0.5-200.5$			$100.5$			$14$			$-1$			$-14$							$200.5-400.5$			$300.5 (a)$			$15$			$0$			$0$							$400.5-600.5$			$500.5$			$14$			$1$			$14$							$600.5-800.5$			$700.5$			$7$			$2$			$14$							Total			-			$\Sigma f_i = 50$			-			$\Sigma f_i u_i = 14$			Here,assumed mean $a = 300.5$,class width $h = 200$,and total observations $N = 50$.Using the step-deviation formula:Mean $(\bar{x}) = a + h 	imes \left( \frac{\Sigma f_i u_i}{\Sigma f_i} ight)$$\bar{x} = 300.5 + 200 	imes \left( \frac{14}{50} ight)$$\bar{x} = 300.5 + 4 	imes 14$$\bar{x} = 300.5 + 56 = 356.5$Thus,the mean daily income is $Rs. 356.5$.

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 $0$	$34$

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

Marks	Number of students
Below $10$	$10$
Below $20$	$50$
Below $30$	$130$
Below $40$	$270$
Below $50$	$440$
Below $60$	$570$
Below $70$	$670$
Below $80$	$740$
Below $90$	$780$
Below $100$	$800$

The daily income of a sample of $50$ employees is tabulated as follows:

Income (in $Rs.$) $1-200$ $201-400$ $401-600$ $601-800$

Number of employees $14$ $15$ $14$ $7$

Find the mean daily income of the employees. (in $.5$)

Similar Questions

The mean of ungrouped data and the mean calculated when the same data is grouped are always the same. Do you agree with this statement? Give reason for your answer.

The median of the following frequency distribution is $525$ and the total frequency is $100$. Find the missing frequencies $x$ and $y$.

Class $0-100$ $100-200$ $200-300$ $300-400$ $400-500$ $500-600$ $600-700$ $700-800$ $800-900$ $900-1000$

Frequency $2$ $5$ $x$ $12$ $17$ $20$ $y$ $9$ $7$ $4$

Rachana had an average score of $45$ from $6$ tests. Her teacher dropped her lowest score,which is $30$,and calculated the average of the remaining scores to decide her grade. Which of the following gives her new average score?

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Income (in $Rs.$)	$1-200$	$201-400$	$401-600$	$601-800$
Number of employees	$14$	$15$	$14$	$7$

The daily income of a sample of $50$ employees is tabulated as follows: Income (in $Rs.$) $1-200$ $201-400$ $401-600$ $601-800$ Number of employees $14$ $15$ $14$ $7$ Find the mean daily income of the employees. (in $.5$)