Statistics: How to find standard deviation and mean if you only know ∑x and ∑x^2

The actual question is:
The daily mean wind speed, x (kn) for Leeming is recorded in June 2015. The summary of the data is:
∑x = 243 and ∑x^2= 2317

a)use your calculator to work out the mean and standard deviation of the daily mean wind speed in June 2015.

I don't understand how I'm supposed to do this if I don't know the frequency or wind speeds?

You need the number of samples (days in June). You can then calculate the SD:

${\sigma}^2=\frac{1}{n}\sum{(x-\bar{x})^2}$

$\therefore n {\sigma}^2=\sum{(x^2-2x \bar{x}+\bar{x}^2)}=..$

Use $\bar{x}=\frac{1}{n}\sum{x}$