466. Find the corrected sample variance for the given sample distribution $n=10$:

$$
\begin{array}{lccc}
x_{i} & 102 & 104 & 108 \\
n_{i} & 2 & 3 & 5
\end{array}
$$
Solution. Let's switch to conditional variants $u_{i}=x_{i}-104$. In the end, we will get the distribution

$$
\begin{array}{lrll}
u_{i} & -2 & 0 & 4 \\
n_{i} & 2 & 3 & 5
\end{array}
$$

Let's find the corrected sample variance of the conditional variants:

$$
s_{u}^{2}=\frac{\sum n_{i} u_{i}^{2}-\left[\sum n_{i} u_{i}\right]^{2} / n}{n-1}
$$

Substituting the conditional variants, their frequencies, and the sample size into this formula, we get $s_{u}^{2}=6.93$:

All the original variants were reduced by the same constant number $C=104$, so the variance did not change, i.e., the sought variance is equal to the variance of the conditional variants: $s_{X}^{2}=s_{u}^{2}=6.93$.