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A stock index is a numerical representation of the way a group of stocks has performed relative to some base reference date in the past. They are calculated in two ways, weighted or unweighted. Unweighted indices are simple arithmetic or geometric averages. With an arithmetic average all the percentage changes in the prices of the constituent stocks are added and then divided by the number of stocks in the index. The geometric average is calculated by multiplying all the prices of the shares in the index and taking the nth root where n is the number of prices that have been multiplied. (The nth root of a number A is a number B such that when n copies of B are multiplied together the result is A). With weighted indices certain stocks carry a greater weighting than others, usually based on their market value or market capitalization.
See also: Market-value Weighted Index, Price Weighted Index