Currently, I have the following information

- Standard deviation = 1.6667
- Size of set = 4
- Average = 2.5

From the following number set A : {1, 2, 3, 4}

- Standard deviation = 1.6667
- Size of set = 4
- Average = 1.5

From the following number set B : {0, 1, 2, 3}

Now, I do not have the detailed element information in both set A and set B. I do not know set A is having {1, 2, 3, 4}. I also do not know set B is having {0, 1, 2, 3}.

What I only know is, the Standard deviation, Size of set and Average for set A and B.

Now, I would like to compute the Standard deviation for the combination of set A and set B. (Of course, there should be no problem in computing Size of set and Average of set A and set B). Is it possible to do so?