[I got this problem from Ernie Cohen, who I think had made it up. Itay Neeman suggested the use of "clans" instead of Ernie’s original "families", because "clans" has a stronger connotation of the groups being disjoint.]
The people in a country are partitioned into clans. In order to estimate the average size of a clan, a survey is conducted where 1000 randomly selected people are asked to state the size of the clan to which they belong. How does one compute an estimate average clan size from the data collected?