Math Help - calculation standard deviation using propogation of error help?

1. calculation standard deviation using propogation of error help?

Given the following values for xi and yi
{xi}= 3.4, 1.3, 2.3, 1.9, 3.1, 2.5, 3.2, 4.5, 4.7, 4.3
{yi}= 2.3, 4.2, 6.4, 3.9, 4.7, 3.6, 1.7, 3.7, 5.3, 5.8

If $p_{i} = x_{i} + y_{i}$

$q_{i} = x_{i} - y_{i}$

and $z_{i} = x_{i} \times y_{i}$

Calculate the mean and standard deviation for p, q and z using the propagation of error method. (i.e. use the mean value and the standard deviation of x and y to calculate the mean and standard deviation of p, q and z)

I know how to calculate standard deviation, however I dont how to do it using the mean value and standard deviation from my first results? How is that even possible?

How can I calculate stadard deviation from standard deviation?

2. Here I have attached the answers, but not sure how they got the standard deviation of p q and z.