Shown below is a histogram of a simple coin flip experiment where someone flips a coin 20 times and records what they see each time. Now repeat this a bunch of times.



As you can see, what you might think happens, since the chance of getting heads is 50% we see the highest probability at 10 which is 50% of 20 trials and also the expected value E(X) of the random Variable X.

Variance would be the width of the number of outcomes with probabilities higher than 0, or negligibly 0. In this case between 4 and 16. The wider the range the higher the variance, and vice versa.