If the standard deviation of 0,1,2,3 .......9 is ' k ' then the standard deviation of 10,11,12,13 ,....... 19 will be

Step-by-step solution

The standard deviation of a set of observations x₁, x₂, ..., x_n is given by = 1 n _ i=1 ^ n (x_i - x )^2 . Let the first set of observations be X = 0, 1, 2, ..., 9 . The standard deviation of this set is k . The second set of observations is Y = 10, 11, 12, ..., 19 . Each element y_i in set Y can be written as y_i = x_i + 10 , where x_i is the corresponding element in set X . The standard deviation is invariant under a change of origin. If each observation in a data set is increased by a constant c , the standard