I did an binomial experiment to flip 10 coins and count the total number of heads.This was repeated 200 times.However at the end of the 200 tries, i noticed that the biased sample variance is actually closer to my population variance.Why is this so? Isn't the unbiased variance supposed to be closer to the population variance? The population variance is 2.5, while the biased variance is 2.7,unbiased variance is 2.77.

Also, if instead of 10 coins, we flip 5 coins each time, what will be the difference theoretically?