We verified the validity of the empirical method to derive the 4He abundance used in our previous papers by applying it to CLOUDY (v13.01) models. Using newly published HeI emissivities, for which we present convenient fits as well as the output CLOUDY case B hydrogen and HeI line intensities, we found that the empirical method is able to reproduce the input CLOUDY 4He abundance with an accuracy of better than 1%. The CLOUDY output data also allowed us to derive the non-recombination contribution to the intensities of the strongest Balmer hydrogen Halpha, Hbeta, Hgamma, and Hdelta emission lines and the ionisation correction factors for He. With these improvements we used our updated empirical method to derive the 4He abundances and to test corrections for several systematic effects in a sample of 1610 spectra of low-metallicity extragalactic HII regions, the largest sample used so far. From this sample we extracted a subsample of 111 HII regions with Hbeta equivalent width EW(Hbeta) > 150A, with excitation parameter x = O^{2+}/O > 0.8, and with helium mass fraction Y derived with an accuracy better than 3%. With this subsample we derived the primordial 4He mass fraction Yp = 0.254+/-0.003 from linear regression Y-O/H. The derived value of Yp is higher at the 68% confidence level (CL) than that predicted by the standard big bang nucleosynthesis (SBBN) model, possibly implying the existence of different types of neutrino species in addition to the three known types of active neutrinos. Using the most recently derived primordial abundances D/H = (2.60+/-0.12)x10^{-5} and Yp = 0.254+/-0.003 and the chi^2 technique, we found that the best agreement between abundances of these light elements is achieved in a cosmological model with baryon mass density Omegab h^2 = 0.0234+/-0.0019 (68% CL) and an effective number of the neutrino species Neff = 3.51+/-0.35 (68% CL).
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