The given survey conducted on 25 households in a locality provides data on the number of households falling within different ranges of a variable, indicated by the values of x and y. We are asked to find the values of x and y when the mode is 4. Let's analyze the given data and solve the problem step by step.

1. Understanding the data:
The data is presented in ranges, and each range is associated with a frequency (number of households). The ranges are as follows:
- 1-3: 7 households
- 3-5: x households
- 5-7: y households
- 7-9: 2 households
- 9-11: 1 household

2. Finding the mode:
The mode is the value that appears most frequently in the data. In this case, the mode is given as 4. It means that the range with the highest frequency should contain the value 4.

3. Analyzing the data:
From the given data, we can observe that the range 1-3 has a frequency of 7 households, which is the highest frequency. Therefore, the mode is 4.

4. Determining the values of x and y:
Since the mode is 4 and it falls within the range 1-3, the values of x and y can be determined by considering the remaining ranges.

- For x: Since the range 1-3 has a frequency of 7 households, and the remaining ranges have a total frequency of 3 households (2 in the range 7-9 and 1 in the range 9-11), the value of x should be 3.

- For y: The remaining households (25 - 7 - 3 - 2 - 1) should fall within the range 5-7, which means the value of y is 12.

5. Final answer:
After analyzing the given data, we have determined that the value of x is 3 and the value of y is 12.

In summary, the given survey data on 25 households in a locality helps us determine the values of x and y. By considering the mode, which is 4, and analyzing the frequency of households in each range, we find that x is 3 and y is 12.