6. In the measurement process, due to errors from measuring instruments and human observation, the obtained data has errors compared to the true value, so only approximate values can be obtained. For the data obtained from multiple measurements $a_{1}, a_{2}, \cdots, a_{n}$, it is usually necessary to calculate its "best approximate value" $x$ (the best approximate value $x$ minimizes the "sum of the squares of the differences between $x$ and these $n$ approximate data points $a_{1}, a_{2}, \cdots, a_{n}$"), then this "best approximate value" $x=$ $\qquad$
6. $x=\frac{a_{1}+a_{2}+\cdots+a_{n}}{n}$
$$
f(x)=\left(x-a_{1}\right)^{2}+\left(x-a_{2}\right)^{2}+\cdots+\left(x-a_{n}\right)^{2}=n\left(x-\frac{a_{1}+a_{2}+\cdots+a_{n}}{n}\right)^{2}+\left(a_{1}^{2}+a_{2}^{2}+\cdots+\right.
$$
$\left.a_{n}^{2}\right)-\frac{\left(a_{1}+a_{2}+\cdots+a_{n}\right)^{2}}{n}$. When $x=\frac{a_{1}+a_{2}+\cdots+a_{n}}{n}$, $f(x)$ is minimized.