Percentages and Distributive Law?

[handlep]

Hi everyone, and first of all, please forgive me if I am posting this question in the wrong area. I hope someone can advise me on this please.

I am sure that it is not correct to 'average' out a set of percentages? So for example, I don't think you should take 46%, 72%, 88% and 65% and say, the average percentage is 67.75%. And I think the reason it is wrong is something to do with Distributive Law (but only because that is what someone told me, so I don't know how correct that is).

Can someone please advise me on whether it is, or is not, correct to average percentages, and if it's not, explain why?

Many thanks in advance for any help.

Pete.

 

[stapel]

You can take the average of any set of numerical values. With respect to percentages, how else would one, for instance, determine his average quiz score? :wink:

I have no idea how this might relate to the Distributive Law. :shock:

Eliz.

 

[Deleted member 4993]

Hi everyone, and first of all, please forgive me if I am posting this question in the wrong area. I hope someone can advise me on this please.

I am sure that it is not correct to 'average' out a set of percentages? So for example, I don't think you should take 46%, 72%, 88% and 65% and say, the average percentage is 67.75%. And I think the reason it is wrong is something to do with Distributive Law (but only because that is what someone told me, so I don't know how correct that is).

Can someone please advise me on whether it is, or is not, correct to average percentages, and if it's not, explain why?

Many thanks in advance for any help.

Pete.

In general, you cannot "directly" calculate "average" of averages.

For example

you drove from point A to B - 60 miles at average speed of 60 mph in a time 1 hrs.

Then you drove B to C - 60 miles at 30 mph in a time 2 hrs.

So your average speed from point A to C is (120/3 =) 40 mph.

Which is clearly different from the "average of the average speeds".

If the denominators in the samples (time in case of average speed, no of specimens in case of other averages), then it works that "average of averages" will be equal to the "true average".

When we talk about %, in a sense we talk about averages. Suppose in atest there were 8 problems - worth 15 points each - and you scored 100 - so your scored 83.33%

And in the next test there were 4 problems worth 20 points each and you scored 75 (93.75%)

Your "true" average score is (175/200=) 87.5%.

However, averages of % gives you 88.5%.

 

[handlep]

Hi Eliz, thanks for responding. OK, let's ignore the DL reference, that could be a total red herring.

Let's look at this:

On my first score, I get 70 out of 186 (37.634%)
On my next score, I get 94 out of 299 (31.438%)
On my next score, I get 43 out of 310 (13.87%)
On my next score, I get 13 out of 487 (2.669%)

So (and let's ignore the fact that the scores are abysmal ), the average of those percentages is 21.4%

But, I have scored a total of 220 out of a possible 1282 = which is 17.16%. If each of the scores had been out of the same figure (i.e. 70/100, 94/100, 43/100 and 13/100), then averaging would work, but I don't think it does if you just take a group of averages. Apologies if I didn't explain clearly first time.

 

[handlep]

Hi Subhotosh Khan, thanks for your response. OK, so that seems to bear out what I have just said in my reponse to Eliz, if the denominators are equal, it will work, otherwise not.

Thanks again.

 

[stapel]

On my first score, I get 70 out of 186 (37.634%)
On my next score, I get 94 out of 299 (31.438%)
On my next score, I get 43 out of 310 (13.87%)
On my next score, I get 13 out of 487 (2.669%)

So (and let's ignore the fact that the scores are abysmal ), the average of those percentages is 21.4%

But, I have scored a total of 220 out of a possible 1282 = which is 17.16%.

Well, which are you trying to find? The average of your scores so far, or your overall progress in the course so far (and perhaps what score you need on the final in order to attain some desired overall grade)? These are two different things which, naturally, use two different methods leading to two different answers. :shock:

We cannot determine the method or answer until you decide the question! :wink:

Eliz.