The mean is arguably the most commonly used measure for central tendency, no no, don’t fall asleep! important point ahead.
We routinely compute the average as an estimate for the mean. All else constant, how much return should we expect the S&P 500 to deliver over some period? the average of past returns is a good answer. The average is the Maximum Likelihood (ML) estimate under Gaussianity. The average is a private case of least square minimization (a regression with no explanatory variables). It is a good answer. BUT:
is suppose to reflect the relation between a stock and the general market. A broad based index such as the S&P 500 is often taken as proxy for the general market. The ![\[stock_i = \beta_0+\beta_1market_i+e_i\]](https://eranraviv.com/wp-content/ql-cache/quicklatex.com-22e1828ad7a9577c9a80d84f27f05f35_l3.png "Rendered by QuickLaTeX.com")
of say, 1.5 means that when the market goes up 1% the specific stock goes up 1.5%. (Ignoring all the biases at the moment!)