The mean of a set of 30 observations is 75. If each observation is multiplied by a non-zero number \lambda and then each of them is decreased by 25, their mean remains the same. The \lambda is equal to
Solutions · 1
Official solution
As mean is a linear operation, so if each observation is multiplied by \[\lambda \] and decreased by 25 then the mean becomes 75\[\lambda \] −25.
According to the question,
75λ−25 = 75⇒λ=34