To find the modes of this data set, we need to determine the number(s) that appear most frequently. Let's count the frequency of each number:
Number of pets: 1 (frequency: 4)
Number of pets: 2 (frequency: 3)
Number of pets: 3 (frequency: 1)
Number of pets: 4 (frequency: 2)
From this count, we can see that the number 1 appears most frequently (four times). Therefore, the mode of this data set is 1.
Hence, the mode of this data set is 1.