There is a number beside the current bid price and a number beside the current ask price. Do these numbers represent the volume of trades completed at the bid and ask prices or pending completion?
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The numbers that you are referring to are the bid and ask volume and they represent the size of the market at current price.
For example, the current NBBO is $10 x $11 with a size of 8 x 7. That means that one or more people are looking to buy 800 shares at $10 and one or more people are looking to sell 700 shares at $11.
If you were to place an order to buy 500 shares at $10.25 then the quote would become $10.25 x $11 with a size of 5 x 7

Bob Baerker
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βThe numbers that you are referring to are the bid and ask volume...β Shouldn't that say "bid and ask size"? β TainToTain Apr 17 '19 at 22:13
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"Buy volume" is used interchangeably with "ask volume" (shares offered for sale at a specific price) and conversely for "sell volume" and "bid volume." The most common phrase used to describe this is market size as you indicated. β Bob Baerker Apr 17 '19 at 23:26