Consider the following distribution of daily wages of 50 workers of a factory.
| Daily wages (in ₹) | 500 - 520 | 520-540 | 540 - 560 | 560 - 580 | 580 - 600 |
|---|---|---|---|---|---|
| Number of workers | 12 | 14 | 8 | 6 | 10 |
Find the mean daily wages of the workers of the factory by using an appropriate method.
To find the mean daily wages, we use the Direct Method. First, we calculate the class mark () for each class interval by finding the midpoint (average of upper and lower limits).
The calculation table is as follows:
- For 500-520: ,
- For 520-540: ,
- For 540-560: ,
- For 560-580: ,
- For 580-600: ,
The total number of workers is and the sum of the product of values is .
Using the formula: Mean () =
Therefore, the mean daily wage of the workers is ₹ 545.20.
Explanation
The solution follows the Direct Method as illustrated in Table 13.3 of the provided context. This method is appropriate here because the class size is uniform and the numerical values are manageable. We calculate the class mark () for each interval, multiply it by the frequency (), sum these products, and divide by the total frequency to find the mean.
Solution Steps
Step 1: Calculate the class mark () for each wage interval (e.g., for 500-520, ).
Step 2: Compute the product for each class and find the sum .
Step 3: Verify the total frequency .
Step 4: Apply the mean formula .