Certainly! Let's go through the detailed steps to understand the solution to this question.
We are given the daily wages of workers along with the number of workers corresponding to each wage range. The aim is to find the weighted average of the daily wages.
1. Daily Wages and Number of Workers:
- Daily wages [in Rs]: [450, 550, 650, 750, 850] (These are the midpoints of the given wage ranges: 400-500, 500-600, 600-700, 700-800, and 800-900)
- Number of workers: [35, 50, 30, 25, 18]
2. Calculate the weighted sum of the daily wages:
To find the weighted sum, we multiply each daily wage by the corresponding number of workers and then add these products together.
[tex]\[
\begin{aligned}
\text{Weighted Sum} & = (450 \times 35) + (550 \times 50) + (650 \times 30) + (750 \times 25) + (850 \times 18)\\
& = 450 \times 35 + 550 \times 50 + 650 \times 30 + 750 \times 25 + 850 \times 18\\
& = 15750 + 27500 + 19500 + 18750 + 15300\\
& = 96800
\end{aligned}
\][/tex]
3. Calculate the total number of workers:
We add up the number of workers in each category.
[tex]\[
\text{Total number of workers} = 35 + 50 + 30 + 25 + 18 = 158
\][/tex]
4. Calculate the weighted average of the daily wages:
The weighted average is obtained by dividing the weighted sum by the total number of workers.
[tex]\[
\text{Weighted Average} = \frac{\text{Weighted Sum}}{\text{Total number of workers}} = \frac{96800}{158} \approx 612.66
\][/tex]
So, the final weighted average of the daily wages is approximately Rs. 612.66.
