To calculate the approximate average income of the respondents, we'll use the midpoint of each income group as a representative value for that group. Then, we'll calculate the weighted average based on the number of respondents in each group.

Steps:

1. Determine the midpoint for each income group:

   • $20 to under $30 → Midpoint = $\frac{20 + 30}{2} = 25$ (thousand dollars)
   • $30 to under $40 → Midpoint = $\frac{30 + 40}{2} = 35$ (thousand dollars)
   • $40 to under $50 → Midpoint = $\frac{40 + 50}{2} = 45$ (thousand dollars)
   • $50 to under $60 → Midpoint = $\frac{50 + 60}{2} = 55$ (thousand dollars)
   • $60 to under $70 → Midpoint = $\frac{60 + 70}{2} = 65$ (thousand dollars)

2. Multiply the midpoint by the number of respondents in each group:

   • 25 × 63 = 1575
   • 35 × 112 = 3920
   • 45 × 128 = 5760
   • 55 × 22 = 1210
   • 65 × 35 = 2275

3. Find the total income (sum of the weighted midpoints): $1575 + 3920 + 5760 + 1210 + 2275 = 14740$ (thousand dollars)

4. Find the total number of respondents: $63 + 112 + 128 + 22 + 35 = 360$

5. Calculate the average income: $\text{Average income} = \frac{\text{Total income}}{\text{Total number of respondents}} = \frac{14740}{360} \approx 40.9 \text{ thousand dollars}$

Final Answer:

The approximate average income of the respondents is $40.9 thousand.

Would you like further clarification, or should we proceed to part b?

Here are 5 relative questions you may find interesting:

1. What if the income groups were smaller or larger?
2. How would the average income change if a new group was added?
3. What is the difference between mean and median in this context?
4. How does the weighted average apply to real-world income distributions?
5. Can we predict a respondent's income more accurately using more granular data?

Tip: The midpoint method is a good approximation when dealing with grouped data like income brackets.