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The stock exchange matches buyers and sellers. The stock price is the average price the stock was trading that day. You can sell stock at any price but if it's too high you won't have many buyers.

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Lets say I own a single stock of xyz co, stock is at $25 and I as an ambitious seller decide to sell it at $50 and by a stroke of luck someone makes a fat finger error enters a buy order at $50.

will the stock price tick to $50 for that one transaction ?

It’s a double sided auction so someone who have a sell order at $26 will have priority (Assuming his order has the lowest price), and the stock will tick to $26.

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