The mean of the coefficients of $x, x^{2}, \ldots, x^{7}$ in the binomial expansion of $(2+x)^{9}$ is ___________.

We have, binomial coefficient, $(2+x)^9$ <br/><br/>$T_{r+1}={ }^n C_r 2^{n-r} \times x^r$ <br/><br/>Coefficient of $x\left(T_1\right)={ }^9 C_1 \times 2^8$ <br/><br/>Coefficient of $x^2\left(T_2\right)={ }^9 C_2 \times 2^7$ <br/><br/>Coefficient of $x^3\left(T_3\right)={ }^9 C_3 \times 2^6$ <br/>              .                    . <br/>              .                    . <br/>              .                    . <br/><br/>Coefficient of $x^7\left(T_7\right)={ }^9 C_7 \times 2^2$ <br/><br/>$$ \text { Mean }=\frac{{ }^9 C_1 \times 2^8+{ }^9 C_2 \times 2^7+{ }^9 C_3 \times 2^6+\ldots+{ }^9 C_7 \times 2^2}{7} $$ <br/><br/>$$ \begin{aligned} & { }^9 C_0 \times 2^9+{ }^9 C_1 \times 2^8+{ }^9 C_2 \times 2^7+{ }^9 C_3 \times 2^6+\ldots .+{ }^9 C_7 \times 2^2 \\ & =\frac{+{ }^9 C_8 \times 2^1+{ }^9 C_9 \times 2^0-{ }^9 C_0 \times 2^9-{ }^9 C_8 \times 2^1-{ }^9 C_9 \times 2^0}{7} \end{aligned} $$ <br/><br/>$=\frac{(1+2)^9-2^9-18-1}{7}=\frac{19152}{7}=2736$