The mean of the series x₁, x₂, , x_n is X . If x ₂ is replaced by , then what is the new mean?

Step-by-step solution

Mean of series (x₁, x₂, x₃ x_ n ) aligned & x = x₁+x₂+x₃+ . x_n n & x₁+x₂+x₃+ . x_n=n x aligned Now we will replace x₂ by so no. of elements in series will not change. New series will include and exclude x₂ Hence new series sum : (x₁+x₂+ . . x_n )-x₂+ =n x + -x₂ Now new mean = n x + -x₂ n = n x -x₂+ n