• # question_answer The mean of a set of 30 observations is 75. If each other 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                                            [JEE Online 15-04-2018] A) $\frac{10}{3}$                                  B) $\frac{4}{3}$C) $\frac{1}{2}$                        D) $\frac{2}{3}$

Since mean is a linear operation, after taking product with the same number and subtracting the same number, the mean becomes$75\lambda -25$. We thus have by the condition given in the problem$75\lambda -25=75\Rightarrow \lambda =\frac{4}{3}$.