Scouring the UK census data often leads to various potholes especially around the years of mass migration to Australia and the USA (1840 - 1870).

It's worth remembering that not all who travelled overseas stayed where they landed, or had any intention of staying. Sometimes the intent was purely to solve short term economic problems.

For this reason, records in the 1841, 1851 and 1861 UK census records are sometimes misunderstood or presumed incorrect. Finding a complete family in say 1841 but then not seeing the husband or sons in 1851 or 1861 often leads us to believe there was death sometime in that period.

The "M" matters

Where you see an incomplete family in the later census data and the wife is noted as head of the family, pay attention to her marital status. A "W" means widowed and yes, you can safely assume the husband died. However if it's an "M", meaning married, but the husband is not listed, there is a fair chance the husband was sailing the world trying to find a better life for the family. Check then for shipping records around that time, both outgoing and incoming.  If you find a shipping record that denotes a man as "single", you can't necessarily assume that he wasn't married - it may mean he was just travelling alone and the family stayed at home. Similarly, if you find a wife and children travelling without a husband in the party, this does not always point to the husband being deceased. Assuming death may lead you to miss a wonderful reunification of a family somewhere abroad.