Suppose E(X|Y) and that a figure illustrates expected salary as a function of gender and that it shows that the mean for women is $2500 \$$ and for men is $3500\$$. If $50\%$ are women and $50\%$ men, the variance is 250 000. How to get there, how to calculate the variance and plot the figure?
It is the variance in the means that are meant here.
The random variable being discussed is a sample mean, conditioned over gender.
The mean of this sample mean is $(2500+3500)/2$ which is $3000$.
$$\mathsf E(\bar X)=\sum_x x\, \mathsf P(\bar X{=}x)$$
The variance of the sample mean is $((2500-3000)^2+(3500-3000)^2)/2$ which is $250\,000$.
$$\mathsf{Var}(\bar X)=\sum_x (x-\mathsf E(\bar X))^2\,\mathsf P(\bar X{=}x)$$