Two data set of size 9 and 6 have standard deviation 3 and 4 respectively and arithmetic means 3 and 3 respectively. The standard deviation of combined data set of size 15 is

A

$$\sqrt{\frac{177}{15}}$$

B

$$\sqrt{\frac{175}{15}}$$

C

$$\sqrt{\frac{178}{15}}$$

D

$$\sqrt{\frac{176}{15}}$$