The simple school maths level answer
Never average averages.
The slightly better answer
Never average averages unless the sample sizes of all elements are identical
The reason
suppose you have a set of average speeds for traffic along a road
January 30mph
February 45mph
March 15 mph
What is the average speed for the quarter
You cannot tell as you do not have sufficient information - you might think its (30+45+15)/3 = 30
That is highly unlikely to be correct - for two reasons
1 you don't know the sample sizes
2 speeds are ratios
Now suppose you know that you have
January
Vehicle a 10 miles at 30 mph
Vehicle b 5 miles at 30 mph
vehicle c 25 miles at 30 mph
February
Vehicle d 10 miles at 50 mph
Vehicle e 10 miles at 40 mph
March
vehicle f 25 miles at 15 mph
Total distance travelled = 85 miles
Total time taken (10/30)+(5/30)+(25/30)+(10/50)+(10/40)+(25/15)=
3.45 hours
Average speed= 85/3.45
=~ 24.64 mph