Can you average percentages

Answer 1

My answer comes with the disclaimer that I am in no way an expert, but here goes:

To the simple question, "Can you average percentages," the answer is, yes. But it is important to note, that the average of percentages is not necessarily meaningful. An example here would be helpful, so I am borrowing from this message board http://www.urch.com/forums/gre-math/95834-rezbipul-sum-average-percentage.html.

The example they provide is:

On two of his tests, Harry scored 30 out of a maximum of 50 and on the third he scored 40 out of a maximum of 100? What is his average percentage score on the three tests?

(a) 33.33%

(b) 40%

(c) 50%

(d) 53.3%

(e) 66.66%

So, specifically answering "what is is average percentage score," the answer would be D, 53.3 percent ((.6+.6+.4)/3). I say this is not meaningful, because to get his final percentage score for the class, you would have to use weighted averages. Add up his actual scores, and divide by the total possible points. (30+30+40)/(50+50+100). His final percentage for the class would be 50%, not 53.3%.

Put another way, by Harry scoring 30 out of 50 on two tests, it would be as if he scored 60/100 on one test. Compare this to his 40/100 on the other test, and you get 100/200, or 50%.

I hope this answered your question.

Addition:

The above answer is true, but is not very well explained. What the poster is trying to say is that it is POSSIBLE to average percentages but it is almost never (actually, practically always) not what you want to do. (i.e. don't do it. ever.)

Imagine there are 5000 people in a parade in Minnesota and 20 in Pennsylvania. You know that 2500 out of those 5000 Minnesotans are female, but the 20 Pennsylvanians in the other parade are all male. You want to find out the percentage of females amongst the two parades.

If you average the two percentages:

((2500/5000)+(0/20))/2 = .25

You find that only 25 percent of participants in the two parades are female. But wait, that doesn't make sense- and here's why:

Percentages work on a scale of 0 to 100- they will give no heed to the fact that there are 4980 more people in Minnesota's parade than in Pennsylvania's. From a percentage standpoint, there are 100 things in each.

To solve this and get a good answer, you add up the total amount of females and divide by the total amount of people:

((2500+0)/(20+5000))= .498

Now you can see that there is the logical just-below-one-half answer. This makes sense because there are 2500 females in 5020 people. See what I mean? An average of percentages almost always yields unwanted answers. There are exceptions, but to stay away from causing confusing I will not go into them.