It makes no sense to average together positive and negative P/E ratios. As earnings decrease smoothly, the P/E ratio approaches positive infinity, then experiences a discontinuity (jump) to negative infinity, then increases again toward zero.
To illustrate the absurdity of using arithmetic mean: Two companies with P/E of 35 and one with P/E of -10 would have an averaged P/E of 20, which is better than any single input. That's worse than useless for analysis.
Even for strictly positive P/E values, the inherent non-linearity makes an arithmetic mean a poor statistic.
Instead, you should average the yield: E/P, which may be computed either as 1/(P/E) or by dividing earnings per share by share price. Flip it back to P/E ratio after averaging.