A common task in applied statistics is choosing a parametric model to fit a given set of empirical observations.
However, especially for simple models with few parameters, theoretical predictions may not match empirical observations for higher moments.
Overdispersion is a very common feature in applied data analysis because in practice, populations are frequently heterogeneous (non-uniform) contrary to the assumptions implicit within widely used simple parametric models.
As a more concrete example, it has been observed that the number of boys born to families does not conform faithfully to a binomial distribution as might be expected.
In this case, if the variance of the normal variable is zero, the model reduces to the standard (undispersed) logistic regression.
However, in the case that the data is modeled by a normal distribution with an expected variation, it can be over- or under-dispersed relative to that prediction.
Furthermore in demography, overdispersion is often evident in the analysis of death count data, but demographers prefer the term 'unobserved heterogeneity'.