The variance of 25 observations is 8 . If each observation is multiplied by 3 , then the new variance of the resulting observations is

Let the observations be $x_1, x_2, \dots, x_{25}$. The variance of these observations is given by $Var(X) = \dfrac{1}{n} \sum_{i=1}^{n} (x_i - \bar{x})^2 = 8$.

When each observation is multiplied by a constant $k$, the new observations are $y_i = kx_i$. The new mean is $\bar{y} = k\bar{x}$.

The new variance is $Var(Y) = \dfrac{1}{n} \sum_{i=1}^{n} (y_i - \bar{y})^2 = \dfrac{1}{n} \sum_{i=1}^{n} (kx_i - k\bar{x})^2$.

Factoring out $k^2$, we get $Var(Y) = k^2 \left( \dfrac{1}{n} \sum_{i=1}^{n} (x_i - \bar{x})^2 \right) = k^2 Var(X)$.

Given $k = 3$ and $Var(X) = 8$, the new variance is $3^2 \times 8 = 9 \times 8 = 72$.

Answer: $72$