Question

Question 1: In a factory employing 3000 persons, 5 per cent earn less than Rs.
150 per day, 580 earn from Rs. 151 to Rs. 200 per day, 30 per cent earn from Rs.
201 to Rs. 250 per day, 500 eam from Rs. 251 to Rs. 300 per day. 20 per cent earn
from Rs. 301 to Rs. 350 per day, and the rest earn Rs. 351 or more per day. What is
the median wage?​

Answer 1

Answer:

Step-by-step explanation:

To find the median wage, we need to sort the wage distribution in ascending order and find the middle value. In this case, since 5% of the workers earn less than Rs. 150 per day, that means 150 * 0.05 = 7.5 workers earn less than Rs. 150 per day.

Next, the number of workers earning from Rs. 151 to Rs. 200 per day is 580, so the next 7.5 + 580 = 587.5 workers are in this wage group.

Since 30% of the workers earn from Rs. 201 to Rs. 250 per day, that means 3000 * 0.3 = 900 workers fall into this wage group.

Continuing this way, we can calculate the cumulative number of workers in each wage group. The median wage will be the wage corresponding to the middle value, or the median worker.

Since the number of workers is odd (3000), the median worker will be the (3000 + 1)/2 = 1501st worker.

Since 587.5 workers earn less than or equal to Rs. 200 per day, and 900 workers earn less than or equal to Rs. 250 per day, the median worker must earn more than Rs. 250 per day.

Continuing this way, we can find that the median worker earns Rs. 301 to Rs. 350 per day. Hence, the median wage is Rs. 350.

Answer 2

The median of the data is 242.92

Given:

Number of employed persons in a company 3000  

Here 5 percent earn less than Rs.150 per day,

580 earn from Rs. 151 to Rs. 200 per day,

30 percent earn from Rs.201 to Rs. 250 per day,

500 earn from Rs. 251 to Rs. 300 per day.

20 percent earn from Rs. 301 to Rs. 350 per day, and the rest earn Rs. 351 or more per day  

To find:

The median wage  

Solution:

Formula used:

Median = l+ [ ( (n/2) – cf)/f] × h.

Here 5% of 3000 = (5/100)×3000 = 150

30% of 3000 = (30/100)×3000 = 900

20% of 3000 = (20/100)×3000 = 600    

Now data can be converted as follows

C.I(Wages)         frequency              C.F

0 - 150                     150                   150

151 - 200                 580                  730    (C.F)

201 - 250                900                 1630

251 - 300                500                 2130

301 - 351                 600                 2730    

351 - more              270                  3000      

=> n/2 = 3000/2 = 1500  

=> Median class of the data is [ 201 - 250 ]

 

Median = 201+ [ (1500 – 730)/900 ] × 49

= 201+ [ 770)/900 ] × 49    

= 242.92

Therefore,

The median of the data is 242.92

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