The mean of a set of 30 observations is 75. If each observation is multiplied by a non-zero number λ and then each of them is decreased by 25, their mean remains the same. Then λ is equal to :

Question

The mean of a set of 30 observations is 75. If each observation is multiplied by a non-zero number λ and then each of them is decreased by 25, their mean remains the same. Then λ is equal to : (A) (1/3) (B) (2/3) (C) (4/3) (D) (10/3)

Tardigrade Admin · Accepted Answer

x1+x2+.........+ x30 = 75 × 30 Now given λ(x1+ x2+ x3+ dots dots dots.+ x30) -25 ×30 = 75 ×30 λ( 75 × 30) = 100×30 λ = (4/3)

Q. The mean of a set of $30$ observations is $75$ . If each observation is multiplied by a non-zero number $λ$ and then each of them is decreased by $25$ , their mean remains the same. Then $λ$ is equal to :

$\frac{1}{3}$

$\frac{2}{3}$

$\frac{4}{3}$

$\frac{10}{3}$

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

Q. The mean of a set of 30 observations is 75. If each observation is multiplied by a non-zero number λ and then each of them is decreased by 25, their mean remains the same. Then λ is equal to :

31​

32​

34​

310​