Get quarterly number using monthly number

Question

a,b,c,d,e,f are sales units for January to June and the revenue is p,q,r,s,t,u. The rate can be derived using revenue/units. I have the variances between the rates for all the months(example Variance between Feb and Jan = (q/b - p/a). I do not have any other number in my system but the variances for the 6 months. I need to find the variance between the 2 quarters i.e. [(s+t+u)/(d+e+f)] - [(p+q+r)/(a+b+c)]. is it possible to get the number using only the monthly variances?

Answer 1

I have a feeling that trying to find the variance between quarters [(s+t+u)/(d+e+f)]-[(p+q+r)/(a+b+c)] is not possible to do using just the monthly variances because the farthest apart you can separate the fractions is [s/(d+e+f)] + [t/(d+e+f)] + [u/(d+e+f)] - [p/(a+b+c)] - [q/(a+b+c)] - [r/(a+b+c)] since you cannot separate the denominators apart, only the numerators with the original denominators. It isn't the monthly variance that affects quarterly variance at all, but rather the entire revenue for the quarter over the entire sales of the quarter. Each individual month does not have an effect on the quarter, but the sum of the months revenue over the sum of the months sales units does.