It should be clear that one sheep is sufficient as a sacrificial animal for one man and his family. One sheep or goat will suffice for everyone he intended of his family, whether living or deceased.
One-seventh of a camel or cow is equivalent to one sheep. If a man sacrifices one-seventh of a camel or cow on behalf of himself and his family, that is sufficient. Hence, seven persons can team up to offer one camel or cow on behalf of their families.