I am trying to understand where the famous average return rate of about 10% of the S&P 500 comes from. In most conversations, the usual starting date is on 1965. Its averaging closing value at that time was about 88.16$. Today (2022), it is at 4,343.56$. I then naively attempted to see what the annualized return rate should be to go from the former to the latter (final = initial*(1+x)^years), but I only find something a little over 7%? I then instead tried to look at the return rate per year, from 1965 to 2022, and made an average out of that. This gave me a little over 8%. In any cases, I fail to get to the stated 10%?
I see in some documents that they always state to "include dividends", which may be the source of the error, but this confuses me since the S&P 500 is an index fund and not a single company that could pay dividends?