Question

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

• A. $\frac{10}{3}$
• B. $\frac{4}{3}$
• C. $\frac{1}{3}$
• D. $\frac{2}{3}$

Answer 1

The correct option is B $\frac{4}{3}$

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 $75\lambda -25=75\Rightarrow \lambda =\frac{4}{3}$.

So the correct answer is option B.