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Usefulness of Variance
i know Standard deviation is equal to a constant times the shortest distance from the point $(x_1,x,_2,\ldots,x_n)$ to a line $(r_1,r_2,r_3,\ldots,r_n)$ where the r is equal provide that these objects is in n-dimensional euclidean metric space, it is technically called the geometrical interpretation of the standard deviaiton.
My question is, i know the standared deviation have its remarkable significance in both probability and statistics, so what is the reason to define another term called the variance