• If the prevalence rate of HIV is reduced to half, what will be its impact on life expectancy?

• If all couples follow a stopping rule of a sons and ß daughters, what will be its effect on the sex ratio of the population (Keyfitz, 1968)?

• Are there errors in census age data? What corrections in age data need to be made before using them for prediction of India 's population?

• If the data is available on the proportion married by age, how can one calculate the average age of marriage?

MATHEMATICAL AND STATISTICAL MODELS

Models are mathematical and/or statistical expressions of relationships between variables describing some major, chosen aspects of a phenomenon. In population studies they are often used to explore relationships between different components of demographic systems, and to explore relationship between demographic variables and socio-economic and cultural variables. The relationships expressed in mathematical form of any kind are called mathematical models The Exponential growth model of population (such as P t = P 0 Exp (r.t)) is an example of a simple mathematical model which states that the population growth follows the exponential model. When the relationships are developed using statistical methods such as regression analysis, they are called statistical models. They contain an element of uncertainty. Statistical models have been developed for studying the growth of population as a stochastic process, i.e., a process which can be described only in terms of probability distributions ( Kendall , 1949). Thus statistical models are closer to reality than mathematical models. They are particularly suited for the studies of random errors. Models using probability distributions, Monte Carlo computer simulation methods ( because of their reliance on repeated computation of random or pseudo-random numbers) , regression analysis, discriminant analysis, factor analysis etc. are all statistical models.