What message might these frequent and violent changes leadership have sent to people living outside roman empire

The primary message this would have sent was that the Empire was in danger of collapsing, since it was beyond clear that the rulers could not control their own population. 

1920 census

the census was scheduled for january the 1st, as the government believed that more farmers would be in their homes by that time instead of april. the census did not ask about unemployment, the number of children, and how long was a couple married were not taken into consideration. individuals were considered as residents of the places they normally slept, not the places were they worked at or visited.

2010 census

the census was scheduled for april 1st, 2010. it was the shortest census in history: it only contained 10 questions related to name, age, gender, ethnicity, relationship, and whether the citizen owned a home or rented one. the government launched a website in order to provide the citizens with information regarding the census. there were also "teach census weeks" in schools nationwide.