When creating an index, it must be decided what criteria will affect the value of the index, and in the case of a price-weighted index, the only consideration is the price of shares.
A price-weighted index is created by adding up the individual price per share of the companies included in the index and dividing by the number of companies. Essentially what you've done is arrived at the average price per share of the companies included in the index.
What isn't as obvious about this is the weighting that this gives each stock relative to its price, because when the companies with larger share prices experience fluctuations in price, it affects the index disproportionately to fluctuations in price from companies with lower price-per-share, even though the company with a lower price per share might have a larger market capitalization.
For this reason, there are other weighting methods, such as cap-weighting, but price-weighting is a viable method and has always been used by the Dow Jones Industrial Average.
Interestingly, the 30 stocks that make up the DJIA do not mean that the prices are added up and divided by 30, but in fact the prices are added up and divided by a Divisor that they have arrived at to accommodate for the long history and changes to the companies included in the index, and this gives the value of the index some continuity over time.
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