In this paper, we have determined necessary and sufficient Tauberian conditions under which statistically convergence follows from statistically $(C,1)$-convergence of sequences of fuzzy numbers. Our conditions are satisfied if a sequence of fuzzy numbers is statistically slowly oscillating. Also, under additional conditions it is proved that a bounded sequence of fuzzy numbers which is $(C,1)$-level-convergent to its statistical limit superior is statistically convergent.