I?m curious about how The price of stock is set. I don?t mean the
process of brokers buying/selling their client?s stock; I want to know
how ?The? price of a stock, the price that, for however briefly,
appears on tickers all over the world, is set. I?m guessing it is an
average of the stock price being bought and sold over some amount of
time but I?m looking for the exact (or as quantitative as possible)
answer/algorithm. A little explanation with possibly a link, if
applicable, would be great.

The ticker you see is just a moment in time.  The update rate is set. 
So what you see as a stock scrolls by is a moment in time where a
buyer decides to buy and a seller decides to sell.  It is this one
transaction that is reported.

Hi

The value on the ticker is determined by the last value traded.  The
brief moment is determined by how often it is traded.  If the stock is
traded often, then the ticker changes value often if it's is traded
very little then the price fluctuate within a certain range. The
fluctution within a certain range is determined by the "SPECIALIST" on
the floor.  You will have to look up that yourself.

If you were to buy stock of company xyz now for $5.00 at the NYSE,
then the ticker around the world will show $5.00 if technology is fast
enough.  There lies the problem because nowadays because a hot stock
can be traded faster than the ticker can change.  Basically, the price
on the ticker is the suppose to be the price of the last known share
traded.

Now if you are meaning to ask how the price of a company is valued,
then that's up to each individuals. However, there are some some
accounting standards to understand and ad hoc analysis that's
involved.