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Duration is another way to measure bond volatility. Duration is a measure of how much the price of a bond changes when compared to its interest rate. Bond price will change from time to time as the issuing organization evaluates the value of the bond on the market.
Volatility is Usually Standard Deviation, Not Variance. In finance, volatility is usually understood as standard deviation. Of course, variance and standard deviation are very closely related (standard deviation is the square root of variance), but the common interpretation of volatility is standard deviation of returns, and not variance. Here you can find more details: