Would anyone be kind enough to tell me show to calculate the standard deviation of a rate per 1000

For instance

A hospital ward has

In Jan 20 days of Flu within 20 bed days

In Feb 50 days of Flu within 80 bed days

In March 100 days if flu within 200 bed days

So the average number of days of flu per 1000 bed days=

(20+50+100)*1000/(20+80+200)=566.6667

Hopefully having that correct I need to know the formula to calculate the standard deviation

Any help would be great!