1.4. For what $x$ does the function $f(x)=\left(x-a_{1}\right)^{2}+\ldots+\left(x-a_{n}\right)^{2}$ take its minimum value?
1.4. It is clear that $f(x)=n x^{2}-2\left(a_{1}+\ldots+a_{n}\right) x+a_{1}^{2}+\ldots+a_{n}^{2}$. This quadratic trinomial takes its minimum value at $x=$ $=\frac{a_{1}+\ldots+a_{n}}{n}$.