Study of statistics of births, deaths, disease to show the state of community

One word substitute is Demography.

Geography: the study of the physical features of the earth and its atmosphere, and of human activity as it affects and is affected by these, including the distribution of populations and resources and political and economic activities.
Anthropology: the study of human societies and cultures and their development.
Topography: the arrangement of the natural and artificial physical features of an area.
Demography: the study of statistics such as births, deaths, income, or the incidence of disease, which illustrate the changing structure of human populations.