The daily income of a sample of 50 employees | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(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 $Rs. 356.5$.

Daily income (in Rs.)	$100-120$	$120-140$	$140-160$	$160-180$	$180-200$
Number of workers	$12$	$14$	$8$	$6$	$10$

Marks	$0-10$	$10-20$	$20-30$	$30-40$	$40-50$
No. of students	$20$	$10$	$20$	$30$	$20$

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

$\sum_{i=1}^{10} (x_i - \bar{x}) = \dots$

In a maths test taken by $40$ students,the average score of $30$ boys is $16$ and the average score of $10$ girls is $12$. Which of the following gives the average score of the whole class?

For a given frequency distribution,$\Sigma f_{i} d_{i} = -50$,$\Sigma f_{i} = 200$ and $A = 62.5$. Then the mean $\bar{x} = $ ........

The following distribution gives the daily income of $50$ workers of a factory.
Daily income (in Rs.) $100-120$ $120-140$ $140-160$ $160-180$ $180-200$
Number of workers $12$ $14$ $8$ $6$ $10$

Convert the distribution above to a less than type cumulative frequency distribution,and draw its ogive.

Calculate the mean of the frequency distribution of the marks scored by $100$ students in a mathematics test:

Marks $0-10$ $10-20$ $20-30$ $30-40$ $40-50$

No. of students $20$ $10$ $20$ $30$ $20$

Vedclass Test Series

Exam Paper Generator

Online Exam Module

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 $.5$)