Context: Flare-accelerated electrons may produce closely temporarily related hard X-ray (HXR) emission while interacting with the dense solar atmosphere and radio type III bursts when propagating from the low corona to the interplanetary medium. The link between these emissions has been studied in previous studies. We present here new results on the correlation between the number and spectrum of HXR-producing electrons and the type III characteristics (flux, starting frequency). Aims: The aim of this study is to extend the results from previous statistical studies of radio type III bursts and associated HXR emissions: in particular, to determine what kind of correlation, if any, exists between the HXR-emitting electron numbers and the radio flux, as well as whether any correlations between the electron numbers or energy spectra are deduced from associated HXR emissions and type III starting (stopping) frequencies. Methods: This study is based on thirteen years of data between 2002 and 2014. We shortlisted ≃200 events with a close temporal association between HXR emissions and radio type III bursts in the 450–150 MHz range. We used X-ray flare observations from RHESSI and Fermi /GBM to calculate the number of electrons giving rise to the observed X-ray flux and observations from the Nançay Radioheliograph to calculate the peak radio flux at different frequencies in the 450–150 MHz range. Under the assumption of thick-target emissions, the number of HXR-producing electrons and their energy spectra were computed. The correlation between electron numbers, power-law indices, and the peak radio fluxes at different frequencies were analysed as well as potential correlations between the electron numbers and starting frequency of the radio burst. Bootstrap analysis for the correlation coefficients was performed to quantify the statistical significance of the fit. Results: The correlation between the number of HXR electrons and the peak flux of the type III emission decreases with increasing frequency. This correlation is larger when considering the electron number above 20 keV rather than the electron number above 10 keV. A weak anti-correlation is also found between the absolute value of the electron spectral index and the peak radio flux at 228 MHz. A rough correlation is found between the HXR-producing electron number above 20 keV and the type III starting frequency. This correlation is smaller if the electron number above 10 keV is considered. All the results are discussed in the framework of results from previous studies and in the context of numerical simulations of bump-in-tail instabilities and subsequent radio emissions.