How to calculate root mean std dev given 2 readings?

Hello

I am at a loss as to how to work out a rsmd (for 52 weeks) given a rsmd for 20 and 32 weeks.

The question is:

In a certain district, the mean annual rainfall is 80cm, with standard deviation 4cm.

Jake, a local meteorologist, kept a record of the weekly rainfall in his garden. His first data set, comprising 20 weeks of figures resulted in a mean weekly rainfall of 1.5cm. The rmsd was 0.1cm. His second set of data, over 32 weeks, resulted in a mean of 1.7cm and a rmsd of 0.09cm.

Calculate the overall mean and the overall rmsd for the whole year.

For the annual mean I calculate as ((20 x 1.5) + (32 x 1.7)) / 52 = 1.62cm. The answer book gives same answer so I assume this is correct way to calculate.

My calculation for annual rmsd was:

((20 x 0.1) + (32 x 0.09)) / 52 = 0.094 - which is incorrect. Book answer gives 0.135. How would I calculate the annual rmsd (root mean standard deviation)?

Angus