To estimate the number of persons having incomes between 2000 and 2500, we need to make use of the given data and apply linear interpolation. Here's how we can do that:

Step 1: Analyze the given data.

We have the following income ranges and the corresponding number of persons:

We are interested in the income range between 2000 and 2500, which falls within the 2000–3000 income range.

Step 2: Apply linear interpolation.

We assume that the number of persons is uniformly distributed within the 2000–3000 income range. Thus, to estimate the number of people in the 2000–2500 range, we can interpolate from the 1500 people who fall in the 2000–3000 range.

The proportion of the interval from 2000 to 2500 within the 2000–3000 range is: $\frac{2500 - 2000}{3000 - 2000} = \frac{500}{1000} = 0.5$ This means that 50% of the people in the 2000–3000 income range earn between 2000 and 2500.

Step 3: Calculate the number of people between 2000 and 2500.

Now, we multiply the total number of persons in the 2000–3000 range by 0.5 to get the number of people earning between 2000 and 2500: $\text{Number of persons} = 0.5 \times 1500 = 750$

Final Answer:

The estimated number of persons having incomes between 2000 and 2500 is 750.

Would you like further details or have any questions?

Here are five related questions to expand on this topic:

1. How would the answer change if the distribution within the income ranges was non-uniform?
2. Can you explain the concept of linear interpolation in more detail?
3. How could we estimate the number of people in the range 2500–3000?
4. What other methods could be used to estimate the number of people in a specific range?
5. How would you graphically represent this distribution?

Tip: When using linear interpolation, always check that the data is uniformly distributed, as assumptions of uniformity may lead to inaccurate results if the distribution varies significantly.