Observe a random variable X very many times. In the long run, the proportion of outcomes taking any value gets close to the probability of that value. The Law of Large Numbers says that the average of the observed values gets close to the mean μX of X. In this applet, we represent a random variable X as the total number of spots on the "up" faces of one or more dice.
This site provides a simulation of the law of large numbers. The site also provides a visualization along with the simulation.
Type of Material:
Simulation
Recommended Uses:
This activity can be used in class, or for homework, during lecture, group work or individually. This activity can be also used to clear up misconceptions.
Technical Requirements:
The app works on any browser with JavaScript enabled.
Identify Major Learning Goals:
The purpose of this site is to provide learners of the conceptual understanding that no matter how many tries or the outcome of each try, or even the number of dice, the value of the sample mean will always approach the value of the population mean. Specifically the goals are:
Get an intuitive feel for the Law of Large Numbers.
Recognize the difference between many trials and a trial with many possible outcomes.
Target Student Population:
College General Ed, College Lower Division, College Upper Division.
The target population for this activity would be anyone in a lower level statistics course.
Prerequisite Knowledge or Skills:
Some prerequisite knowledge includes the definition of the mean, notation for the mean, definition of the sample mean, and the population mean, and the differences between the two.
Content Quality
Rating:
Strengths:
The great part of this activity is the illustration of using dice as a real life example. Students should be able to quickly relate and picture the experiment as if they were really doing it.
This site is a wonderful visualization of the Law of Large Numbers in action. Using the example of rolling dice will ensure that every student understands the experiment. It is very visual and interactive allowing the student to select how many dice to roll and how many times to roll them.
Concerns:
Perhaps the contect should have a bit more concept building just in case the student is completely unaware. If this activity was given to a student with minimal prerequisite knowledge, they might have a difficult time following along.
Potential Effectiveness as a Teaching Tool
Rating:
Strengths:
Once the learners have a conceptual understanding of terms, this simulation is very effective and the learning goals are easily identified.
Students using this applet will quickly learn the punchline of the Law of Large Numbers. Within a couple of minutes, the students will be able to participate in the activity and grasp the concept.
Concerns:
It would be helpful to have links to further exploration and use of the Law of Large Numbers.
Ease of Use for Both Students and Faculty
Rating:
Strengths:
The site is very easy to use and the directions are very clear and specific. Navigation is easy. Learners should be able to navigate this layout easily.
There are clear instructions provided at the top of the page that lets the students know what they are supposed to learn. Since there are only seven very clearly labeled pieces of the applet that the students can use to make the exploration happen, students will easily navigate through the activity. The results are also clearly displayed.
Creative Commons:
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