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The volume of a security is the number of units traded in a period of time, typically one day. If the volume of Honda (HMC) stock was 400,000 today, that means 400,000 shares were purchased and 400,000 were sold (each trade is the result of one buy and one sell and counts only once).
Volume is used to judge the strength of a price change. If a stock increases 5% in value with high volume, it's regarded as more significant because more money (more people) bought into the change. A 5% increase with low volume means less money (fewer people) bought in to the change. Volume also indicates the liquidity of an asset. High volume makes it easier to sell more units of the asset without driving the price down (slippage).
Related Links
Investopedia's definition of volume
Wikipedia's article on volume
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