1. Toss a coin 10 times and after each toss, record in the following table the result of the toss and the proportion of heads so far. For example, suppose you obtain the following sequence of heads and tails for the first five tosses: H T T T H. After the first toss, the proportion of heads so far is one out of one: 1/1 or 1. After the second toss, the proportion of heads so far is one out of two: 1/2. After the third toss, the proportion of heads is one out of three: 1/3. After the fourth toss, the proportion of heads is one out of four: 1/4. After the fifth toss, the proportion of heads is two out of five: 2/5.
Toss # 1 2 3 4 5 6 7 8 9 10
H/T T H H H H T T H H T
Prop of H so Far 0/1 1/2 2/3 3/4 4/5 4/6 4/7 5/8 6/9 6/10
2. On the following axes, plot the proportion of heads so far, for each toss from your table. What does the graph show?
The plot shows that in the first few tosses the proportion can vary widely but overtime the proportion becomes normalized. Given enough time the plot will stabilize around 0.5
3. Now, you will use Excel to simulate 1000 independent tosses of a fair coin and plot on a graph the proportion of heads so far after each toss using the instructions that follow #3.
4. Write a paragraph explaining what your graph shows.
Like I said in part 2, the graph begins with pretty wild and large differences in proportion but quickly begins to stabilize. Eventually this experiment ended with the proportion being around 52% of the coin tosses landing on heads. Again as the number increases, the likelihood of it eventually stabilizing at exactly 50% becomes more likely.
5. Put the cursor in any blank cell near your graph. Press Ctrl= to change the random numbers and your graph. Do this several times and describe how the graph changes.
The graph usually has a different erratic pattern at the beginning, it varied from 0.3 to 0.7. Usually the proportion stabilized...