Chuprov was born in Mosal'sk but grew up and was educated in Moscow where his father, Alexander Ivanovich (1842–1908), a distinguished economist and statistician, was a professor.
Alexander Alexandrovich graduated from the physico-mathematical faculty of Moscow University in 1896 with a dissertation on "The theory of probability as the foundation of theoretical statistics."
His doctoral dissertation, supervised by Georg Friedrich Knapp (1842–1926) Die Feldgemeinschaft, eine morphologische Untersuchung was published in 1902.
On his return to Russia and, in order to get a teaching position, Chuprov completed master's examinations at the University of Moscow, concentrating on theoretical economics and the application of mathematical methods.
In January 1919, he became director of the statistical bureau of the Central Union in Stockholm and in charge of its publication Bulletin of World Economy.
The curriculum he designed for the St. Petersburg Polytechnic Institute was modern and his book on the theory of statistics was influential.
Bortkiewicz was the leading exponent of the dispersion theory of Lexis and Chuprov contributed to this research.
In John Maynard Keynes' Treatise on Probability (1921) he is put with Markov and Chebyshev as the three great Russian names in the theory of statistics.
The richest source of information about Chuprov is Oscar Sheynin's article: (The same website now [2007] also offers a downloadable version, in Russian, of the recently discovered Bortkiewicz-Chuprov correspondence 1895–1926.)