A sample of 35 observations has the mean 80 and standard deviation is as 4. A second sample of 65 observations has mean 70 and S.D as 3. The S.D of combined sample is  is _________

Here $n_1=35,\overline{x_1}=80,{\sigma }_1=4; n_2=65,\overline{x_2}=70,{\sigma }_2=3$ 
 $$\begin{gathered} combined \overline{x}=\frac{n_1\overline{x_1}+n_2\overline{x_2}}{n_1+n_2}=73.5 \\ {\sigma }^2=\frac{n_1\left({\sigma }_1^2+d_1^2\right)+n_2\left({\sigma }_2^2+d_2^2\right)}{n_1+n_2} \left(\because d_1=\overline{x_1}-\overline{x},d_2=\overline{x_2}-\overline{x}\right) \end{gathered}$$ 
$$\begin{gathered} =\frac{35(16+42.25)+65(9+12.25)}{100}=34.20 \\ \sigma =\sqrt{34.2}\Rightarrow n=34.2 \\ 5n=171 \end{gathered}$$