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Frequently Asked Questions...

Averaging percentages: looking for mathematical term?

I am looking to find out if there is a mathematical term for the gulf between the two following figures.

Figure 1:
500,000 / 1,000,000 = 50%
30,000 / 2,000,000 = 1.50%
Average of 50% & 1.50% = 25.75%.

Okay so 25.75% is an average of the percentages.

Figure 2:
500,000 + 30,000 = 530,000
1,000,000 + 2,000,000 = 3,000,000
530,000 / 3,000,000 = 17.67%
So this second model sums up the totals before calculating the percentage, so it isn't an average.

So my question is, is there a term that describes the difference between 17.67% and 25.75%? Or is there nothing else but to say that 25.75% is an average and 17.67% is not?

The reason I ask is because I need to explain to a large group of people why a 25.75% average is so much higher than 17.67%. I would qualify 17.67% as being a more accurate figure. Is there a name I can apply to this effect?


Best Answer...

Answer:

the term you are looking for in the second calculation is

WEIGHTED AVERAGE

why this term is apt will be clear
from another way of calculation

the 1st denominator is 1 million
and the 2nd is 2 million
now if we give a 1 : 2 weightage for the PERCENTAGES calculated in the first way, the result is
[1/3]*50 +[2/3]*1.5 = 53/3 % = 17.67 %