The United Nations has data on every country's household size and statistics. Use the drop-down menu at the top (see picture above) to choose your country.
The World Population Review has family household data on countries and states in the US. Use the search box in the upper right corner to look up any state or country.
Try searching for a specific country in Britannica. Then use Command+F to search for specific words, for example, family, household.
The CIA World Factbook has a lot of data on different countries. Use the magnifying glass to search your subject, for example: family composition, households.
Search for a country in this database, and you will get many reference sources that will give you information on household sizes, family compositions, and trends in those areas.