We studied the time-averaged gamma-ray burst spectra accumulated by the spectroscopy detectors of the Burst and Transient Source Experiment. The spectra are described well at low energy by a power-law continuum with an exponential cutoff and by a steeper power law at high energy. However, the spectral parameters vary from burst to burst with no universal values. The break in the spectrum ranges from below 100 keV to more than 1 MeV, but peaks below 200 keV with only a small fraction of the spectra breaking above 400 keV; it is therefore unlikely that a majority of the burst spectra are shaped directly by pair processes, unless bursts originate from a broad redshift range. The correlations among burst parameters do not fulfill the predictions of the cosmological models of burst origin. No correlations with burst morphology or the spatial distribution were found. We demonstrate the importance of using a complete spectral description even if a partial description (e.g., a model without a high-energy tail) is statistically satisfactory. Associated Articles Part 1 Part 2 Part 3 Part 4