# Conceptual difference between weighted arithmetic mean and ordinary arithmetic mean

I'm having a hard time understanding what does these values really represents, most about the weighted mean actually. I will give an example:

In a factory there's 2 equipments:

Equipment 1 produces 100 tons in 10 hours

Equipment 2 produces 100 tons in 2 hours

If we calculate the arithmetic mean that's easy as (100 + 100) / (10 + 2) = 16,6 t/h.

If we calculate the weighted arithmetic mean on volume, that should be:

 (50t/h * 100t + 10t/h * 100t) / (100t + 100t)
= 6000t²/h / 200t =
= 30t/h


Ok, now what does these values really mean? The arithmetic mean, 16,6t/h, I think it simply means that each hour of the day we will have 16,6 tons of the product being produced, is that correct? Now what about the 30 t/h? Is it right to think that after one hour of the day I will have 30 tons of the product? How so?

Thanks!

• Your ordinary mean won't be reliable in calculating any unit which is measured per ton, assuming both machines run for the same amount of time because five times as much of your output will be produced by the faster machine. By giving the faster machine more weight your weighted mean reflects the fact that that machine accounts for 5 times as much output. – samerivertwice May 18 '18 at 19:09
• If both machines run simultaneously then 1 produces 10 tons per hour and 2 produces 50 tons per hour giving a combined 60 tons per hour. This mean only makes sense for continuous simultaneous production. If 1 runs for 10 hours THEN 2 for two hours your first calculation is correct - over that12 hours they produced 16.6 tons per hour. Your 30 tons per hour is simply the average of the two production rates (10 per hour and 50 per hour) - this is the original 60 tons per hour split between 2 machines or the average hourly rate per machine. – Paul May 18 '18 at 19:18