<P> The standard deviation of the sum of two random variables can be related to their individual standard deviations and the covariance between them: </P> <Dl> <Dd> σ (X + Y) = var ⁡ (X) + var ⁡ (Y) + 2 cov ⁡ (X, Y). (\ displaystyle \ sigma (X + Y) = (\ sqrt (\ operatorname (var) (X) + \ operatorname (var) (Y) + 2 \, \ operatorname (cov) (X, Y))). \,) </Dd> </Dl> <Dd> σ (X + Y) = var ⁡ (X) + var ⁡ (Y) + 2 cov ⁡ (X, Y). (\ displaystyle \ sigma (X + Y) = (\ sqrt (\ operatorname (var) (X) + \ operatorname (var) (Y) + 2 \, \ operatorname (cov) (X, Y))). \,) </Dd> <P> where var = σ 2 (\ displaystyle \ scriptstyle \ operatorname (var) \, = \, \ sigma ^ (2)) and cov (\ displaystyle \ scriptstyle \ operatorname (cov)) stand for variance and covariance, respectively . </P>

What does it mean to have a standard deviation of 10