He was a distinguished mathematical statistician whose wide-ranging research included the analysis of martingale inequalities, Markov processes, de Finetti's theorem, consistency of Bayes estimators, sampling, the bootstrap, and procedures for testing and evaluating models.

Freedman also wrote widely on the application—and misapplication—of statistics in the social sciences, including epidemiology, public policy, and law.

Freedman was a consulting or testifying expert on statistics in disputes involving employment discrimination, fair loan practices, voting rights, duplicate signatures on petitions, railroad taxation, ecological inference, flight patterns of golf balls, price scanner errors, bovine spongiform encephalopathy (mad cow disease), and sampling.

He consulted for the Bank of Canada, the Carnegie Commission, the City of San Francisco, the County of Los Angeles, and the Federal Reserve, as well as the U.S. departments of energy, treasury, justice, and commerce.

Freedman and his colleague Kenneth Wachter testified to the United States Congress and the courts against adjusting the 1980 and 1990 censuses using estimates of differential undercounts.

Two of his earlier results (1963 and 1965) investigate whether or not and under what circumstances a Bayesian learning approach is consistent, i.e. when does the prior converge to the true probability distribution given sufficiently many observed data.