The statistical distributions of main-sequence multiple-star properties reveal invaluable insights into the processes of binary star formation, and they provide initial conditions for population synthesis studies of binary star evolution. Binary stars are discovered and characterised through a variety of techniques. Correcting for their respective selection effects and combining the bias-corrected results is not a trivial process. This is partially because the intrinsic distributions of companion frequency, primary mass M1, orbital period P, mass ratio q and eccentricity e are all interrelated , i.e., f(M1,P,q,e)/= f(M1)f(P)f(q)f(e). In particular, the binary fraction increases with primary mass, especially across short orbital periods, and binaries become weighted towards larger eccentricities and more extreme mass ratios with increasing separation, especially for more massive primaries. Moreover, binary star statistics vary with age, environment and metallicity. This chapter summarises the strengths and limitations of the various observational techniques, and reviews the statistical correlations in the intrinsic (bias-corrected) multiple-star properties.