(10 pts) There is an important perspective to communicate regarding the taking of "samples from a population". We imagine that there is a theoretical "population" of all possible outcomes of (for example) 10 coin flips, with respective probabilities for each possible outcome, and an associated "true" mean and "true" standard deviation. However, when we flip 10 coins, we don't see the population as a whole... we only see one sample from the population. If we take LOTS of samples, then the average number of heads should begin to converge to the "true" mean, and the standard deviation of our samples should begin to converge to the "true" standard deviation. Of course, the mean should be half as many heads as coin flips (5 in this case), if we have an honest coin. But, then, one shouldn't be too surprised if any one sample comes up with 6, 7, or even 8 heads. This is because the standard deviation is quite large, relatively speaking, since the number of flips is very modest. Comment on trends you see in your data which relate to these principles.
C. (5 pts) As hinted in the introduction, there is a very important rule of thumb for statistical processes that you should learn: the size of the fluctuations is proportional to the SQUARE ROOT of the number of data points. In this case, it turns out that the theoretical "true" standard deviation for coin flips is half of the square root of the number of flips F, like so:
