Question

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. Then $\lambda$ is equal to :

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

Answer 1

Answer: (C)

$x_{1}+x_{2}+.........+ x_{30} = 75 \times 30$
Now given $\lambda\left(x_{1}+ x_{2}+ x_{3}+\dots\dots\dots.+ x_{30}\right) -25 \times30 = 75 \times30$
$\lambda\left( 75 \times 30\right) = 100\times30$
$\lambda = \frac{4}{3}$