The problem (translated from Swedish, the correct mathematical terms might not be written but I will do my best):
" For two sets of data $x_1,...,x_5$ and $y_1,...,y_9$ pre-calculated values are:
$\bar x=12.2 $ and $s_x=2.1$
$\bar y=15.8$ and $s_y=2.9$
(where $s_x$ and $s_y$ is the standard deviation for the x and y data)
You now want to combine the data to one larger data $z_1,..., z_{14}$
Calculate the mean value and standard deviation for the new combined data. "
What I have come up with
For the mean value I calculate it like this:
$\frac{12.2\times5+15.8\times9}{9+5}=14.51=\bar z$
This is correct according to the book, however, I do not know how to calculate the standard deviation, the correct answer is $s_z=13.2$