The mean of a set of 30 observation is 75 . If each observations is...

Let $30$ observations be ${x}_{1}, {x}_{2}, . . . . . \ldots , {x}_{30}$.

Given mean $= 75$

$⇒ {x}_{1} + {x}_{2} + \ldots + {x}_{30} = 75 \times 30$

Now according to question,

$\dfrac{\lambda ( {x}_{1} + {x}_{2} + \ldots + {x}_{30} ) - 25 \times 30}{30} = \dfrac{75 \times 30}{30}$

$⇒ \lambda\left(75 \times 30\right) = 100 \times 30$

$⇒ \lambda = \dfrac{4}{3}$