Question

I once did an experiment in the classroom, comparing Theoretical or Classical and Empirical Probability. We had six teams and each team was instructed to toss a coin 100 times and record their outcomes. Some teams had results as different as 70 heads, 30 tails or vice versa, while others had results close to the theoretical 50/50 expectation. When we listed all of the team results on the board and added them together, the grand total came very close to the 300 heads and 300 tails, 50% probability. So, the Empirical results (actual) can diverge from the Theoretical or Classical in the short run, but over the long run the two should agree unless the coins are biased.
Regards,

Answer 1

This is the principle on which the central limit theorem is based. According to this, when you take many samples of a size 'n', and plot them the resulting distribution is approximately normal with mean equal to the mean of the original population.

Here you have only performed this experiment 6 times ( because there were only 6 teams). If you had performed this experiment even more number of times, the result would have been even better than the one you obtained with just 6 teams.

This is because a normal distribution is symmetric around the mean, so when you take many samples from a population, some of them will lie above the mean and some of them will lile below. But the overall mean would still come close to the original mean, if the number of samples are large.

The more the number of samples you take, the lesser is the difference between the expected and the observed mean.