Users toss a virtual coin or a virtual die to investigate the law of averages. The applet graphs the percentage of successes observed in 1 to 10000 tosses. The outcomes of multiple experiments (consisting of 10000 tosses each) can be graphed on the same plot to faciliate visualization of trends. Activities are provided to facilitate thinking about the law of averages with the applet.
Users toss a virtual coin or a virtual die to investigate the law of averages. The applet graphs the percentage of successes observed in 1 to 10000 tosses. The outcomes of multiple experiments (consisting of 10000 tosses each) can be graphed on the same plot to faciliate visualization of trends. Activities are provided to facilitate thinking about the law of averages with the applet.
Instructions:
In illustration of the law of averages, you will observe that as the number of trials increases, the percentage of successes approaches the expected percentage of successes while the difference between the observed and expected number of successes increases.
Scale - Note that the scale on the horizontal axis is not constant. The plots may appear to show sudden jumps or dramatic differences at 100 and 1000 tosses, this is a result of the change of scale at those positions.
Display – The 'Display' menu in the upper left hand corner of the applet allows the user to adjust the speed of the experiments and change the appearance of the plot.
Coin Activity
Select the 'coin' radio button on the applet. Press the 'Get data' button to toss the coin 10000 times, do this several times so the results of a number of experiments are overlain in the plot. Use the plots to respond to the prompts below.
1. Move between the plot display radio buttons ('show %heads' et al.) as needed to answer the following questions.
2. Are you more likely to get exactly 50% heads in 10 tosses or 1000 tosses of a coin? Explain.
Die Activity
Select the 'die' radio button on the applet. Press the 'Get data' button to roll the die 10000 times, do this several times so the results of a number of experiments are overlain in the plot. Use the plots to respond to the prompts below.
1. Move between the plot display radio buttons ('show %threes' et al.) as needed to answer the following questions.
2. Are you more likely to get exactly the expected percentage of threes in 10 rolls or 1000 rolls of a die? Explain.