In this paper, the procedure for determination of the mean value of non-homogenous background radiation and the expression of measurement uncertainty is considered. The background radiation is described using the Student's distribution, and the measurement uncertainty using the Welch-Satterthwaite equation. The proposed algorithm was experimentally verified under well-controlled laboratory conditions and satisfactory results were obtained. [Project of the Serbian Ministry of Education, Science and Technological Development, Grant no. 171007]