"The family" is a singular noun, referring to the group as a whole. Since it's singular, you need the singular verb "was."
Here's why it works:
* Subject-Verb Agreement: The subject of the sentence is "The family" and the verb is "was." They agree in number (singular).
* Collective Noun: "The family" is a collective noun, representing a group of individuals. While it refers to multiple people, it functions as a single unit in this sentence.
Example:
"The family was having dinner when the doorbell rang."