In this extended abstract, we introduce a concept of statistically quasi-Cauchyness of a sequence in X in the sense that a sequence (xk) is statistically quasi-Cauchy in X if limn→∞ 1n |{k ≤ n : d(xk+1, xk) − c ∈ P}| for each c ∈P where (X, d) is a cone metric space, and P denotes interior of a cone P of X. It turns out that a function f from a totally bounded subset A of X into X is uniformly continuous if f preserves statistically quasi-Cauchy sequences.