62G30, 62G32, 60F15.

In this paper, we consider the record statistics at the time when the nth record of any kind (either an upper or lower) is observed based on a sequence of independent random variables with identical continuous distributions of bounded support. We provide sharp upper bounds for expectations of record range and current upper record increment. We also present numerical evaluations of the so obtained bounds. The results may be of interest in estimating the expected lengths of the confidence intervals for quantiles as well as prediction intervals for record statistics.;