$\begin{array}{ll} & \text { Mean }+ \text { variance }=\frac{15}{2} \\ & \Rightarrow n p+n p q=\frac{15}{2} \\ & \Rightarrow n p+n p(1-p)=\frac{15}{2} \quad \ldots[\because p+q=1] \\ & \Rightarrow n\left(2 p-p^2\right)=\frac{15}{2} \\ & \Rightarrow 2 p-p^2=\frac{15}{2 \times 10} \quad \ldots[n=10] \\ & \Rightarrow 4 p^2-8 p+3=0 \\ & \Rightarrow(2 p-3)(2 p-1)=0 \\ & \Rightarrow p=\frac{3}{2} \text { or } p=\frac{1}{2} \\ & p=\frac{1}{2}...[0 < p < 1] \\ & q=1-\frac{1}{2}=\frac{1}{2} \\ & \text { Variance }=n p q=10 \times \frac{1}{2} \times \frac{1}{2}=2.5\end{array}$