Finding average of denominator knowing average of numerator and average of fraction

Question

Good day to you all. I have a little problem I have been banging my head on for a while.

I have come to think that it is impossible, but I hope you can save me.

I have a fraction, $ \frac{num_i}{den_i} $., which takes different values over time.

The objective is to calculate $ \frac{average(num_i)}{average(den_i)} $.

I have at my disposal $ average (\frac{num_i}{den_i}) $ and $average(num_i) $

Is there any way to do this, or do I need to get $average(den_i)$ also?

Thanks a lot for your help.

Edit with an example

Let's take $\frac {1}{2},\frac{1}{3},\frac{1}{4}$

The information at my disposal is:

• The average of numerators is 1.
• The average of fractions is 0.36

Is it possible with the information I have to retrieve the average of denominators?

Answer 1

No, consider the example:

$A=\{{1\over2},{1\over3},{1\over6}\}$

$B=\{{1\over2},{1\over4},{1\over4}\}$

We have the numerator average $1$ and fraction average $1\over3$ for both cases yet average for denomiators are not the same.

Answer 2

This is impossible.

First case, consider the series $\frac{1}{2},\frac{2}{6}$.
Then, $avg(num)=\frac{3}{2}, avg(den)=4, avg(num/den)=\frac{5}{12}$ and $avg(num)/avg(den)=\frac{3}{8}$.

Second case, consider the series $\frac{2}{4},\frac{1}{3}$.
Then, $avg(num)=\frac{3}{2}, avg(den)=\frac{7}{2}, avg(num/den)=\frac{5}{12}$ and $avg(num)/avg(den)=\frac{3}{7}$.

In both cases your two givens are the same, but the answer is different. Therefore you cannot find the answer from the givens.

Edit: I see you got another answer that was both faster and better. Well done.