What quantity did you change?
Labs / Mathematics
Central Limit Theorem
Pick a parent distribution — even a lumpy or lopsided one — then set how many values go into each average. Every sample mean drops into the lower histogram, and as it fills in you'll see those averages pile up into a bell shape centered on the true mean, no matter how strange the parent looked.
Labs / Mathematics / Central Limit Theorem
Central Limit Theorem
Pick a parent distribution — even a lumpy or lopsided one — then set how many values go into each average. Every sample mean drops into the lower histogram, and as it fills in you'll see those averages pile up into a bell shape centered on the true mean, no matter how strange the parent looked.
Why it matters
Why explore this?
Mathematics helps us describe patterns precisely and predict what comes next. This model turns an abstract relationship into something you can change and observe.
Explore
Try the model
samples 0x̄ —SE —shape —
Investigate
Questions to test
Predict first, try it in the model, then use what you observe to answer.
What to try
- Start on the Right-skew parent with n = 1. The averages look just as skewed — so where does the bell shape actually come from?
- Slide n up to 30. Why does the sampling distribution get narrower and more symmetric at the same time?
- The standard error readout drops as n grows. Does it halve when you double n, or does it take four times as many samples to halve it?
- Switch to the Bimodal parent — two separate humps. How can the average of two humps end up as a single bell centered between them?
- Turn on the Normal curve overlay. For which parent and which n does the real histogram hug the predicted bell almost perfectly?
Explain
Make sense of what happened
State the pattern in words, test it with another example, and then connect it to the mathematical rule or representation shown in the model.
Check
Before you leave
What pattern did you observe?
Does the pattern work for another example?
If you can answer all three using evidence from the model, you understand the main idea. If not, return to Explore and change one setting at a time.