An explanation of the Central Limit Theorem, why it is of such importance, and how it impacts data. Includes an applet to demostrate the CLT in practice for a number of different distributions. Four distributions (Uniform, Normal, Skewed, Bimodal) may be used. Sample size and number of samples can be changed. For the bimodal, distribution, some changes can be made to the shape of each side. The x-bars are plotted to show how this distribution approximates a normal distribution.
Type of Material:
Simulation, reference material
Recommended Uses:
Supplemental material within an introductory statistics course. Could be shown to whole class or assigned as outside activity. Because of the large amount of text, it seems better as part of a homework assignment, although just the apple may be useful in the classroom.
Technical Requirements:
Java
Identify Major Learning Goals:
To learn about and understand the impact of the Central Limit Theorem, to see how it works when applied to various distributions, and to visualize how the sample means for non-normal distributions will approximate the standard normal.
Target Student Population:
Introductory to intermediate statistics students.
Prerequisite Knowledge or Skills:
It may be necessary for students to have an understanding of the following terminology: population parameter, sample mean, sample standard deviation.
Content Quality
Rating:
Strengths:
Excellently written introduction that assumes no prior knowledge for the reader, but still will be useful for someone who has had a basic introduction to the material before. The applet is very nicely designed.
The information on the web site provides a nice introduction to the reason this is important. Clear visualization with the graph of population and sample means on same screen.
Concerns:
The page is very word-heavy; which makes it difficult for a novice student to digest. The applet lacks in customization and does not work on an iPad.
Potential Effectiveness as a Teaching Tool
Rating:
Strengths:
The article is very self-contained and a student could learn all the material on their own. The concepts are described both from a very intuitive level and a mathematical level, which can appeal to different types of students. As a self-contained object, it would be very easy to integrate into a class as homework to ease the lecture on the topic.
Concerns:
The applet contains many numerical summaries; far more than the student is introduced to in the text. This may be confusing for a new student. Also, it does not seem possible for a faculty (or student) to know if the student understands the concept after using the applet since there is no assessment. The student may just “push the buttons." There are similar free applets available so it is somewhat redundant in addressing the concept.
Ease of Use for Both Students and Faculty
Rating:
Strengths:
Very easy to use with excellent instructions, and includes some suggested steps to play with. The information on the web page provides sufficient information to use the applet, and the use of the population and sample means graph on the same screen makes it easy to visualize.
Concerns:
The lack of customization makes the applet slightly less interactive. It would be nice if you could generate a custom distribution, rather than just the 4 defaults. Also, the student moves sliders to change sample size and number of samples. Students may not carefully read the information that shows change in number of samples and sample size. The use of the sliders makes it hard to be precise since the number of samples ranges from 1 to 4000 in the narrow space.
Creative Commons:
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