1) A man walking in the woods encounters a stream. Because he is unsure of the stream depth, he measures how deep the water is in many random spots along the entire width of the stream. After 1000 measurements each with a depth of 6 inches, he concludes the probability of the water being 6 inches deep the entire way across to be 100%. Halfway across, the man takes a step and is shocked to find himself in water up to his neck. What mistake did the man make?
3) Someone flips heads on a fair, two-sided coin 100 times in a row. What is the probability that the next flip would also result in a heads? Is it more likely that the next flip would result in tails? Why?
4) Since we see them used so frequently, why do people go to the trouble of computing various statistical measures - for example the mean and standard deviation? What types of insights do they hope to gain by using these measures? Please mention an example of where you have personally used statistical measures in your life - and which measures you used - and what insights you were trying to gain.
5) In what situations might the mean give you a distorted view of the true middle of a range of data? In these instances, which measure would probably give a more accurate picture of the average of a set of data? Why?