Uncertainty

#1
Hi there,

If I take measurements every minute for a whole hour, and I know the uncertainty of a single measurement, is it possible to calculate the uncertainty of the hourly average (the average of the 60 minutely measurements)? I am assuming each measurement and its uncertainty are independent.

From that is it then possible to calculate the uncertainty of a daily average (the average of the 24 hourly measurements) and then also the uncertainty of monthly and yearly averages?

Any help would be appreciated!
 
#2
Is this hourly average uncertainty just going to be the same as the uncertainty of the instrument when it takes its minutely reading?

Eg.

Let's say my instrument has an uncertainty of (+/-) 1 (forget units for now)

Measurement 1 = 8 (+/-)1
Measurement 2 = 6 (+/-)1
Measurement 3 = 13 (+/-)1

Therefore (range including uncertainty)
Measurement 1 = (7,9)
Measurement 2 = (5,7)
Measurement 3 = (12,14)

Average of measurements = 9
Average range (including uncertainty) = (8,10)

Average = 9 (+/-) 1

Is this logic reasonable?