When a total universe with media T is made of two groups with medias K1 and K2, and population fractions X and X2 respectively, it applies that total media, T = K1*X + K2*(1-X) [1] . This means that if we know 3 of the 4 variables (T,K1,K2,X) we may pinpoint the 4th one exactly.
I think this is an important and simple tool in statistical teaching and theory because it mixes concepts like medias, fractions of population, aggregated coherence, sets theory and practical analysis. I have used it to detect statistical manipulations about income and poverty reports of the government of my country, Colombia (just published).
Do you have other simple answers and comments to this question that I may not have seen in statistical books, papers, and text-books? (Note: Nicholas J. Horton uploaded here in RG: “I hear, I forget. I see, I remember. I do, I understand: a modified Moore-method mathematical statistics course” (September, 24, 2013), a more advanced paper that you may download.)