The chart:
The bar chart tells us that
6 families each have 0 pets,
3 families each have 1 pet,
3 families each have 2 pets,
6 families each have 3 pets,
1 family has 4 pets, and
1 family has 5 pets.
The total number of pets in all these families is \((6\cdot 0)+(3\cdot 1)+(3\cdot 2)+(6\cdot 3)+(1\cdot 4)+(1\cdot 5)=36\). The number of families is \(6+3+3+6+1+1=20\).Therefore, the average number of pets per family is \(\frac{36}{20} = \boxed{1.8}.\)