1. The average score of the participants in a junior high school mathematics competition at a certain school is 75 points. Among them, the number of male participants is $80\%$ more than that of female participants, and the average score of female participants is $20\%$ higher than that of male participants. Therefore, the average score of female participants is  points.
II. 1.84.
Let the number of female participants be $x$, then the number of male participants is $1.8 x$; Let the average score of male participants be $y$ points, then the average score of female participants is $1.2 y$ points. According to the problem, we have $\frac{1.8 x y + 1.2 x y}{x + 1.8 x} = 75$, which simplifies to $1.2 y = 84$.