Question

Daily wages of $110$ workers, obtained in a survey are tabulated below. Compute the mean daily wages and the modal daily wages of these workers.

Daily wages (in $₹$ )	$100 - 120$	$120 - 140$	$140 - 160$	$160 - 180$	$180 - 200$	$200 - 220$	$220 - 240$
Number of workers	$10$	$15$	$20$	$22$	$18$	$12$	$13$

Accepted Answer

We need to find the mean daily wages and the modal daily wages from the given data.

To compute the mean daily wages:

Assumed Mean $a = 170$ . Since, all classes are of equal size, $h = 20$ . We can find the mean daily wages $(x)$ by step deviation method.

Wages (in $₹$ ) Mid-value $(x_{i})$ $u_{i} = \frac{x_{i} - 170}{10}$ $f_{i}$ $10$

$100 - 120$ $12$ $13$ $10$ $- 60$

$120 - 140$ $130$ $- 4$ $15$ $- 60$

$140 - 160$ $150$ $- 2$ $20$ $- 40$

$160 - 180$ $170$ $0$ $22$ $0$

$180 - 200$ $190$ $2$ $18$ $36$

$200 - 220$ $210$ $4$ $12$ $24$

$220 - 240$ $230$ $6$ $13$ $78$

Total $110$ $- 22$

$x = a + h \times \frac{Σ f_{i} u_{i}}{Σ f_{i}} = 170 + (10 \times \frac{- 22}{110}) = 170 - 2 = 168$

To find the modal daily wages:

Maximum class frequency is $22$ , and the class corresponding to this frequency is $160 - 180$ .

We have $h = 20, l = 160, f_{0} = 20, f_{1} = 22, f_{2} = 12$ .

Now, the modal daily wages $= l + \frac{f_{1} - f_{0}}{2 f_{1} - f_{0} - f_{2}} \times h$

$= 160 + \frac{22 - 20}{(2 \times 22) - 20 - 12}$

$= (160 + \frac{1}{6}) = 160.167$

Therefore, the mean daily wages of the workers is $₹ 168$ and the modal daily wages of the workers is $₹ 160.167$ .

Heights (in cm)	$150 - 155$	$155 - 160$	$160 - 165$	$165 - 170$	$170 - 175$	$175 - 180$
No. of students	$15$	$13$	$10$	$8$	$9$	$5$

Important Questions on Sample Question Paper

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Daily wages of 110 workers, obtained in a survey are tabulated below. Compute the mean daily wages and the modal daily wages of these workers. Daily wages (in ₹) 100-120 120-140 140-160 160-180 180-200 200-220 220-240 Number of workers 10 15 20 22 18 12 13

Important Questions on Sample Question Paper

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