To calculate the P/E ratio of a market index such as the S&P500, it is not accurate to take the "simple average" of the P/Es of all stock constituents. The preferred and accurate method is to calculate the weighted average. In this case, each stock's underlying market cap (price multiplied by number of shares in issue) is summed to give the total value in terms of market capitalization for the whole market index.
The same method is computed for each stock's underlying net earnings (earnings per share multiplied by number of shares in issue). In this case the total of all net earnings is computed and this gives the total earnings for the whole market index. The final stage is to divide the total market capitalization by the total earnings to give the market P/E ratio.
The reason for using the weighted average method rather than 'simple' average can best be described by considering a recessionary period of the economic cycle, where a number of stocks would be reporting a loss. For example, a company with a share price of $100, may have made a slight loss of say 10 cents giving a P/E ratio of -1000 (100/0.1). In another case, a company with a share price of $1 may have made a serious loss of 50 cents giving a P/E ratio of - 2 (1/0.5). This mathematical anomaly would create a misrepresentation of the underlying company losses on the overall market index.
