Question

Before you begin this discussion, find a coin and flip it 10 times, recording the outcome of each flip as either heads or tails. Post your results in this discussion, along with the percentage of flips that resulted in heads. We might expect that percentage to be 50%, but the results may vary from student to student (sometimes drastically) in this exercise. As a response to other students, add their data to yours and compute the new percentage of flips that result in heads (You can just make up realistic predictions for the other students). With enough data added, what would you expect to find? What does the central limit theorem have to say about the long-term outcome of exercises like this?

Answer 1

After collection of enough data for the flipping a coin experiment, we might expect that percentages of heads for each student will be near to 0.5 or 50%. These percentage will look somewhat 0.49, 0.51, 0.48, 0.52, 0.47, 0.53, ..etc. If we add all these percentages and find the average for these percentages, then we will get approximately 50% probability of getting a head. For single student or single experiment, probability is varies nearby the actual estimate. But, when we add all these sample estimates and find their expected value or mean of sample proportions, then we will get the percentage approximately equal to 0.5 or 50%.

The central limit theorem says that the average of your sample proportions will be the population proportion. This means, the average of all proportions of heads of coin for all students should be approximately 50%. (This fact holds truer when the sample sizes are over 30.) In other words, if we added enough data for flipping a coin experiment, the average of proportions of heads of a coin for all student will be approximately 0.50 or 50%.