Federated edge learning (FEEL) as an emerging distributed learning paradigm can effectively resolve the resource constraints and privacy issues in the Internet of Things (IoT) by featuring collaborative training at the edge devices under the premise of data localization. Nevertheless, owing to the scarce resources and the inscrutable communication fading, issues such as model damage and signal deviation will critically diminish the convergence performance and learning accuracy of FEEL. With this in mind, reconfigurable intelligent surface (RIS) has recently been integrated to enhance the communication quality of wireless systems by adaptively reconfiguring the signal propagation environment. To utterly release the applied potency of RIS, the configuration of phase shifts is of paramount importance, where accurate channel state information (CSI) is required. Unfortunately, the accurate instantaneous CSI is extremely challenging to be estimated. In this paper, we focus on the realistic scenario assuming only statistical CSI is known, which can be comparatively easily and accurately explored. On the other hand, considering the wireless outage caused by the random non-line-of-sight channel, we rigorously derive an explicit convergence upper bound of the RIS enabled FEEL framework with respect to the outage probability. Based on the convergence theory, a unified resource allocation problem is further established by jointly optimizing bandwidth allocation, and the RIS configuration matrix. Extensive simulations are conducted to demonstrate that the proposed design dramatically promotes the learning performance compared against the baseline solutions.