Schmidt’s Tauberian theorem says that if a sequence (xk) of real numbers is slowly decreasing and $li{m}_{n\to \infty }(1/n){\sum }_{k=1}^n{x}_k=L$, then $li{m}_{k\to \infty }{x}_k=L$. The notion of slow decrease includes Hardy’s two-sided as well as Landau’s one-sided Tauberian conditions as special cases. We show that ordinary summability (C,1) can be replaced by the weaker assumption of statistical summability (C,1) in Schmidt’s theorem. Two recent theorems of Fridy and Khan are also corollaries of our Theorems 1 and 2. In the Appendix, we present a new proof of Vijayaraghavan’s...