\(\overline{X}=\dfrac{5.2+6.5+9.n+10.1}{2+5+n+1}=6,8\)
\(\Leftrightarrow\dfrac{50+9n}{8+n}=6,8\)
\(\Leftrightarrow50+9n=6,8.\left(8+n\right)\)
\(\Leftrightarrow50+9n=54,4+6,8n\)
\(\Leftrightarrow9n-6,8n=54,4-50\)
\(\Leftrightarrow2,2n=4,4\)
\(\Rightarrow n=4,4:2,2=2\)