Assignment 5: Applets and Internet Resources
This assignment explores interactive applets and internet resources that support the teaching and learning of the Central Limit Theorem. As we know, the central limit state that the sampling distribution of the sample means approaches a normal distribution as the sample size gets larger no matter what the shape of the population distribution. Sample sizes equal to or greater than 30 is often considered sufficient under the central limit theorem.
A. Applet Collections
| Title | Description |
|---|---|
| Seeing Theory | An interactive collection of some statistical visualizations concept. It includes activities involving probability distributions, Random variable, Discrete and Continuous variable, sampling distributions, and the Central Limit Theorem. |
| Rossman/Chance Applet | A collection of statistical applets that allows students to explore sampling, probability, randomization, and statistical inference through simulations. |
| Shodor Interactive | A collection of statistical applets that allows students to explore sampling, probability, randomization, and statistical inference through simulations. |
| UBC Central Limit Theorem Visualization | An interactive applet that demonstrates the Central Limit Theorem using real-life situations such as weekly coffee consumption, flu, and voting. Users can change the sample size, draw random samples, calculate sample means, and generate sampling distributions. The applet helps students understand how the distribution of sample means approaches a normal distribution as sample size increases, even when the original population is skewed. |
| Statkey | A collection of statistical simulation tools that helps students investigate sampling distributions, randomization distributions, and statistical inference. |
B. Individual Applets
| Title | Description |
|---|---|
| UBC Central Limit Theorem Visualization | An interactive applet that demonstrates the Central Limit Theorem using real-life situations such as weekly coffee consumption, flu, and voting. Users can change the sample size, draw random samples, calculate sample means, and generate sampling distributions. The applet helps students understand how the distribution of sample means approaches a normal distribution as sample size increases, even when the original population is skewed. |
| Seeing Theory | An interactive collection of some statistical visualizations concept. It includes activities involving probability distributions, Random variable, Discrete and Continuous variable, sampling distributions, and the Central Limit Theorem. |
| Central Limit Theorem for Means – OpenIntro | An interactive applet that allows students to explore the Central Limit Theorem by selecting different population distributions and changing the sample size and number of repeated samples. The simulation demonstrated that the distribution of sample means becomes more concentrated around the population mean and approaches a normal shape as the sample size increases. |
| Central Limit Theorem Explorer | An interactive simulation that allows students to investigate the Central Limit Theorem by selecting a population distribution, adjusting its parameters, and changing the sample size. The applet generates 10,000 random samples and displays the sampling distribution of the sample mean alongside a theoretical normal approximation. |
| GeoGebra | Provides interactive activities that demonstrate how sampling distributions become approximately normal. Choose one specific activity and copy its direct link. |
C. Internet Resources
| Resource | Type | Description |
|---|---|---|
| Numiqo | Interactive simulation | Explore the Central Limit Theorem with three interactive tools: Galton Board, Dice Sum Simulator, and Sample Mean Lab. Adjust sample sizes, trials, and source distributions, and view real-time histograms and density overlays. Compare empirical results with theoretical normal curves to observe convergence and variability |
| SOCR Central Limit Theorem Article | Research article | Discusses an interactive demonstration activity for teaching the Central Limit Theorem |
| Central Limit Theorem in Statistics | Webpage | Explains the Central Limit Theorem using mathematical explanations and visual illustrations, showing how increasing sample size affects the sampling distribution of the mean. |
| But What Is the Central Limit Theorem? – 3Blue1Brown | Video | This educational video uses narration, animations, and practical examples to explain the Central Limit Theorem. It explores how repeated sampling and the addition of random variables lead to approximately normal distributions under suitable conditions. The visual explanations help students understand the relationship between population distributions, sample means, and the normal distribution. This resource is useful for students who prefer learning statistical concepts through watching and listening. |
| Central Limit Theorem – Mental Models Daily | A podcast | A short audio explanation of why sample means become approximately normally distributed as sample size increases. Ideal for an introductory CLT resource. |