# Central limit theorem applet simulation dating

This in-class demonstration combines real world data collection with the use of the applet to enhance the understanding of sampling distribution. Students will work in groups to determine the average date of their 30 coins. In turn, they will report their mean to the instructor, who will record these. The instructor can then create a histogram based on their sample means and explain that they have created a sampling distribution.

Afterwards, the applet can be used to demonstrate properties of the sampling distribution. The idea here is that students will remember what they physically did to create the histogram and, therefore, have a better understanding of sampling distributions.

This demonstration can be used as a first introduction to the concept of sampling distributions. It has been applied at the undergraduate level, but could also be used at the advanced placement level as well.

Including the time spent for viewing the applet, this activity can be completed in a 50 minute class period. Prior to this activity students should be able to calculate the mean and should have seen distributions of many different shapes. Careful planning will make this demonstration go smoothly. Some specific tips include: The activity sheet should be updated to reflect the last full year. If it is currently the sheet should be updated to say The instructor should bring some extra coins.

Even if the students are asked to bring coins, some students may not bring them. Worksheets should be pre-numbered to facilitate calling on the groups. Students should bring a calculator to class to use in calculating averages.

As the students are calculating their averages, the instructor should prepare a histogram on the board or a transparency. The instructor should stress the connection between the histogram created with the average coin dates and the online simulation of the sampling distribution.

Assessment This concept is very deep and can be assessed on several levels. Students can be given a scenario and asked to describe the sampling distribution. Students should also be prompted to explain what makes up the sampling distribution. At the most basic level students should be able to choose a histogram that reflects the sampling distribution of a sample mean. An example of such a Central limit theorem applet simulation dating

can be found in the file: Material on this page is offered under a Creative Commons license unless otherwise noted below.

Define a "Sampling Distribution. Explain that even if the population is very skewed, the average from a large random sample will be normally distributed.

In this activity students are exposed to the concept of sampling distributions by creating a sampling distribution as a class.

By having the students assemble a sampling distribution, they can more readily understand that a sampling distribution is made up of a collection of sample statistics from different samples.

Students are asked to think about the distribution of *Central limit theorem applet simulation dating* dates on U. This distribution should be skewed to the left.

*Central limit theorem applet simulation dating* on the description in the handout, most students will get this idea. If not, an instructor may need to guide them to this point.

This idea will form the basis for illustrating the Central Limit Theorem in later steps. The students then calculate the average of 30 coins to create their own sample statistic. The instructor "assembles" a dot plot or histogram of the sample means created by each student or group.

This is done by calling on each group or individual student to give their sample mean.

The instructor should then mark these on a dotplot or histogram on the board or an overhead. When this histogram is complete, the instructor should point out that the distribution is made up of the means of different samples from the population of interest.

For example, some students may have coins that date back to the s, but the averages will typically be between and The instructor should also point out that there are too few means to clearly see the distribution. This serves Central limit theorem applet simulation dating

a lead into using the applet. The applet can serve as a method to more quickly take samples from the population. The instructor should then open the applet and construct a left skewed distribution resembling the distribution of the individual coin dates.

Point out that these would be equivalent to each sample of coins the class put together. The instructor should point out both the values of the individuals in the second graph and the mean of the sample that appears in blue on the third graph.

The instructor will continue to take samples one at a time until the same number have been taken as were in the histogram assembled by hand.

The instructor can point out that this histogram is crude, due to the small number of Central limit theorem applet simulation dating from which it is constructed. The instructor can use the "" button to take a large number of samples and allow the students to watch the sampling distribution build into an approximately normal distribution. The instructor should point out that even though the parent population is skewed to the left, the distribution of the mean coin dates is approximately normal.

The instructor can repeat the sampling process with different shapes of parent populations. A drop-down menu allows the choice of skewed right, uniform and normal distributions. For each situation, the instructor should point out that regardless of the shape of the parent population, the sampling distribution should be approximately normal.

Finally, the instructor can illustrate how different sample sizes influence the normality of the distribution by repeating the exercise with samples of 5 and Again, the instructor should point out the shape of the distribution.

The activity should conclude with a summary of the demonstration that can be written in their notes.

It is a good idea is to have the students summarize what they have done by filling in the blanks of these sentences: The instructor should have a computer with projector. This demonstration is appropriate for classes as small as 20 students to those large as students. In either, case you want to have at least 20 samples of 30 coins.

For small class sizes students should work on individually.