Week 9: Statistics Extra Credit: Central Limit Theorem

Answer all parts in complete sentences and show all work or explain how you got the values.

Student Learning Outcomes

• The student will demonstrate and compare properties of the central limit theorem

Background Information

The Central Limit Theorem is similar to the Law of Large Numbers. The more samples we take from our sample or the population, the closer our sample resembles a Normal Distribution. When we look at means of samples, it happens even more quickly! In this lab we are looking at 30 values at a time. While the data is being pulled from a larger set, this randomization for the initial set allows for a better change in situation each time. The data you will be using is randomized from 90 values.

The sets are:
Set C1	A random set of 30 individual data values from the original list of 197 values.
Set C5	A random set of 30 means of groups of 5 data values from the original list of 197 values. (i.e. The mean is calculated for a set of 5 randomly selected data values. This is repeated 30 times and those means become your list.)
Set C20	Random set of 30 means of groups of 20 data values from the original list of 197 values. (i.e. The mean is calculated for a set of 20 randomly selected data values. This is repeated 30 times and those means become your list.)

Instructions

The Desmos site below is set up to do all the randomization and calculations for you. Turn off and on the different graphs as needed to see what is happening and to take the individual screenshots for each set.

https://www.desmos.com/calculator/oyvo0cokst

Click the crossed lines button at the top left a few times to see how the histogram, mean, and standard deviation change with each randomization, size, and type of sample. You can also change colors with thegear icon.

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