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What does the weighted average price involved in the settlement price of futures delivery mean and what is the formula?
The weighted average is that each number is multiplied by its share, and then their sum is divided by the number of these numbers.

For example, 5.6.7.8's shares are 20%, 15%, 30% and 35% respectively.

The weighted average is (5 * 20%+6 *15%+7 * 30%+8 * 35%)/4.