Group and Total Average
Ecological fallacy also happens when the average for a group is approximated by the average in the total population divided by the group size. Suppose one knows the number of Protestants and the suicide rate in the USA, but one does not have data linking religion and suicide at the individual level. If one is interested in the suicide rate of Protestants, it is a mistake to consider as an unbiased estimate the total suicide rate divided by the number of Protestants. This estimate implicitly assumes that the suicidal rate of the other religions is zero.
Formally, denote the variable of interest and the mean of the group, we generally have:

However, the law of total expectation gives

This equation must be used to compute a more congent estimate. In this equation, the only things we don't know how to estimate are in blue. We know that, as a probability of suicide, is between 0 and 1. We can plug in this bound and our total estimate in the equation above to obtain an estimate of .
Read more about this topic: Ecological Fallacy
Famous quotes containing the words group, total and/or average:
“Caprice, independence and rebellion, which are opposed to the social order, are essential to the good health of an ethnic group. We shall measure the good health of this group by the number of its delinquents. Nothing is more immobilizing than the spirit of deference.”
—Jean Dubuffet (19011985)
“I think that if most guys in America could somehow get their fave-rave poster girl in bed and have total license to do whatever they wanted with this legendary body for one afternoon, at least 75 percent of the guys in the country would elect to beat her up.”
—Lester Bangs (19481982)
“He seems like an average type of man. Hes not, like smart. Im not trying to rag on him or anything. But he has the same mentality I haveand Im in the eighth grade.”
—Vanessa Martinez (b. c. 1978)