<p>The mathematical foundations and algorithms for determining the sample mathematical expectation of stationary random processes are presented. Functional limitations of algorithms for determining the sample mathematical expectation in binary arithmetic of the Rademacher number-theoretical basis are substantiated. The low speed of computing the sample mathematical expectation in the codes of the Rademacher number-theoretical basis is due to carry operations during the accumulation of sums of the digitized input data from a random process. Lattice models and graphs of rank-sum formation for streaming accumulation of digital data over the sampling interval of a random process are presented. The theoretical foundations of algorithms for determining the sample mathematical expectation in a non-positional number system of the residue class of the Haar–Chrestenson number-theoretical basis are developed. Recommendations are provided for selecting the Haar–Chrestenson code modules that correspond to 4-bit Rademacher basis codes and 8-bit RGB pixel codes of color images. The results of the study enable expanding functionality and increasing the speed of statistical data processing at lower levels of interactive distributed computer systems.</p>