460. Find the sample variance for the given sample distribution of size $n=10$:

$$
\begin{array}{cccc}
x_{i} & 186 & 192 & 194 \\
n_{i} & 2 & 5 & 3
\end{array}
$$
Solution. The options are relatively large numbers, so we will switch to conditional variants $u_{i}=x_{i}-191$ (we subtract from the variant the number $C=191$, close to the sample mean). As a result, we will get the distribution of conditional variants:

$$
\begin{array}{lrrrr}
u_{i} & -5 & 1 & 3 \\
n_{i} & 2 & 5 & 3
\end{array}
$$

We will find the required sample variance:

$$
\begin{aligned}
& D_{\mathrm{B}}=\left(\sum n_{i} u_{i}^{2}\right) / n-\left[\left(\sum n_{i} u_{i}\right) / n\right]^{2}=\left(2 \cdot 5^{2}+5 \cdot 1^{2}+3 \cdot 3^{2}\right) / 10- \\
&-[(2 \cdot(-5)+5 \cdot 1+3 \cdot 3) / 10]^{2}=8.2-0.16=8.04 .
\end{aligned}
$$