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

A

$$\sqrt{\frac{72}{5}}$$

B

$$\sqrt{\frac{68}{5}}$$

C

$$\sqrt{\frac{70}{5}}$$

D

$$\sqrt{\frac{66}{5}}$$