We discuss the construction of minimum variance approximate formulas for a given linear functional. We first describe an elementary method for obtaining the minimum variance weights; for the purpose, we set up two systems having the advantage that the order of the matrix to be inverted will not exceed half the number of abscissas in the formula. A simple interpretation, existence and characterization of minimum variance approximate formulas is given in the space of certain degree polynomials. With the help of this interpretation, we then obtain the minimum variance weights explicitly in terms of certain orthonormal polynomials. We consider minimum variance formulas with equispaced and Chebyshev abscissas; for these abscissas, the orthonormal polynomials are known explicitly and the corresponding minimum variance formulas are obtained explicitly. We give examples of minimum variance formulas for interpolation, numerical differentiation and integration.