Below you will find a collection of dynamic visualizations of statistical ideas.
To browse visualizations, simply click the buttons next to the categories and titles.
In every case you will run the visualization software by clicking on a button.
In some cases you may need to click a button many times to see a long-term pattern emerge (for example, seeing distribution take shape).
To perform repeated trials quickly, simply click on the or button once.
You may then use the enter key to perform more trials.
You may also hold down the enter key to see many trials in rapid succession.
Please note that for the time being, these visualizations work best when using a laptop or tablet.
It is my sincere hope that these visualizations help you to acquire a deeper, more visceral understanding of the ideas covered in a
probability and statistics course.
Sampling
Simple Random Sampling
Random Sampling to Estimate a Mean
Random Sampling to Estimate a Proportion
Stratified Random Sampling
Cluster Sampling
Systematic Random Sampling
Probability
Long-Term Proportion of Heads for a Fair Coin
Long-Term Proportion of "Rolling a Sum of $3$"
Discrete Probability Distribution of a Fair Die
Discrete Probability Distribution of a Crooked Die
Long-Term Average of a Fair Die
Long-Term Average of a Crooked Die $\mu \approx 4.42$
Long-Term Average and Total "Winnings" from Betting $\$1$ on Even in Roulette $\left(\mu\approx -\$0.053\right)$
Long-Term Distribution of a Binomial Random Variable
Long-Term Distribution of Sample Means of a Fair Die (Central Limit Theorem)
Long-Term Distribution of Sample Means of Exponentially Distributed Battery Lives (Central Limit Theorem)
Confidence Intervals
95% Confidence Interval for a Population Mean $\left(\sigma \mbox{ known}\right)$
95% Confidence Interval for a Population Mean $\left(\sigma \mbox{ unknown}\right)$
95% Confidence Interval for a Population Proportion
Tests of Significance
Test of Significance for a Population Mean $\left(\sigma \mbox{ known}\right)$
Test of Significance for a Population Mean $\left(\sigma \mbox{ unknown}\right)$
Test of Significance for a Two Population Means
Dynamic Test of Significance for a Detecting a Loaded Die
Dynamic Test of Significance for Detecting a (Possibly) Crooked Coin