A measure of change
An index can be described as a gauge of the changes in a pool of stocks representing a segment of the market indicating the direction in which the market is heading and what the likely trend might be.
As stocks are components of the overall index, any change in the value of the stock in question will affect the price of the index. So, it follows that a movement in a stock price in an index with fewer components such as the DAX30 will have a greater impact on the overall value of the index compared with that of a larger index such as the S&P500.
Investing in an index can offer traders an easier and cheaper option than investing in every stock within the index itself.