8. If the average of $x_{1}, x_{2}, \cdots, x_{10}$ is 6, and the standard deviation is $\sqrt{2}$, then the range of the average of the data $x_{1}, x_{2}, \cdots, x_{5}$ is $\qquad$ .
8. $[6-\sqrt{2}, 6+\sqrt{2}]$.

From the problem, we know that $x_{1}^{2}+x_{2}^{2}+\cdots+x_{10}^{2}=380$.
Let the average of $x_{1}, x_{2}, \cdots, x_{5}$ be $a$; the average of $x_{6}, x_{7}, \cdots, x_{10}$ be $b$. Then
$$
b=12-a \text {. }
$$

By the Cauchy-Schwarz inequality, we have
$$
\begin{array}{l}
\sum_{i=1}^{5} x_{i}^{2} \geqslant 5 a^{2}, \\
\sum_{i=6}^{10} x_{i}^{2} \geqslant 5 b^{2}=5(12-a)^{2} . \\
\text { Therefore, } 380 \geqslant 5 a^{2}+5(12-a)^{2} \\
\Rightarrow 6-\sqrt{2} \leqslant a \leqslant 6+\sqrt{2} .
\end{array}
$$