Calculate mean. Wage 0 100 100 200 200 300 300 400 400 500 : : : : : : No. of workers 4 12 16 10 8

Calculation of Mean Wage

To calculate the mean wage from the given grouped data, we follow these steps:

Step 1: Find the Midpoints (Class Marks)

The midpoint of each wage interval is calculated using the formula: $$\text{Midpoint}=\frac{\text{Lower limit}+\text{Upper limit}}{2}$$

Step 2: Calculate $f\times x$ (Frequency × Midpoint)

Multiply the number of workers (frequency) by the midpoint of each wage interval.

Step 3: Calculate the Total Frequency (N)

$$N=\sum f=4+12+16+10+8=50$$

Step 4: Calculate the Sum of $f\times x$ (Σfx)

$$\sum fx=200+1800+4000+3500+3600=13100$$

Step 5: Compute the Mean

The formula for the mean of grouped data is: $$\text{Mean}=\frac{\sum fx}{N}$$ $$\text{Mean}=\frac{13100}{50}=262$$

Final Answer

The mean wage of the workers is 262.