If the mean and variance of 8 observations are $9$ and $9.25$ respectively, and each observation is multiplied by $3$, then the new variance of the observations is:

Solution

1. Given the initial variance of the 8 observations is $\text{Var}(x)=9.25$.
2. When each observation is multiplied by a constant $k=3$, the new variance is given by the property $\text{Var}(kx)=k^2\text{Var}(x)$.
3. Substituting the values, we get $$\begin{array}{rl}\text{Var}(3x)& =3^2\times 9.25\\ & =9\times 9.25\end{array}$$.
4. Calculating the product, we find $9\times 9.25=83.25$.
5. Hence the answer is (A).