To find the average earning per workman, we’ll calculate the total earnings for each group and divide by the total number of workmen.

Step 1: Calculate the Total Earnings for Each Group

1. Two workmen paid $5.65 each:
   $2 \times 5.65 = 11.30$

2. Five workmen paid $7.00 each:
   $5 \times 7.00 = 35.00$

3. Four workmen paid $7.25 each:
   $4 \times 7.25 = 29.00$

4. Five workmen (remaining) paid $7.50 each:
   $5 \times 7.50 = 37.50$

Step 2: Calculate the Total Earnings for All Workmen

$11.30 + 35.00 + 29.00 + 37.50 = 112.80$

Step 3: Find the Average Earning per Workman

Since there are 16 workmen, the average earning per workman is: $\frac{112.80}{16} = 7.05$

Answer

The average earning per workman is $7.05.

Would you like more details on any step? Here are related questions you might find helpful:

1. How is the average calculated if the payment varies by group size?
2. How would the average change if the number of workmen in each group changed?
3. Can the average be calculated differently using weighted averages?
4. How do outliers (e.g., one worker paid significantly more or less) affect the average?
5. What if the total earnings needed to be distributed equally afterward?

Tip: In problems with groups and varying payments, organizing each group’s data separately can simplify finding totals and averages.