To calculate the new standard deviation you are correct in saying you need to remember some information about the previous data set.
To calculate the mean of n+1 data points from the mean of n data points is easy, as you've shown.
To calculate the new std dev is also not hard. Remember the definition:
std dev = (1/n) (sum over all data points) ( x - mean ) ^ 2.
The sum can also be written as 2 sums:
(sum over all data points)(x^2) - (sum over all data points)(mean ^2).
You should be able to figure it out from here. Alternatively, you can "remember" the value of "(sum over all data points)(x^2)" and recalculate the std dev as each new data point appears.