📊
Central Limit Theorem
AP Statistics · Unit 5: Sampling Distributions
▶ Auto Sample
⛶ Fullscreen
Population Distribution (one draw shown ●)
Sampling Distribution of x̄ (samples taken: 0)
Samples:
0
x̄ mean:
—
x̄ SD (SE):
—
Theor. SE (σ/√n):
—
Population Shape
Uniform
Right Skew
Bimodal
Normal
Sample Size n
5
Try n=2, n=10, n=30 — watch the magic!
+ 1 Sample
↺ Reset
+ 100 Samples
Auto Speed
Slow
Fast
Turbo
CLT in action:
No matter how weird the population looks, after many samples the x̄ distribution becomes bell-shaped! Increase n to see it narrow.
📝 Quick Quiz
▼
1. The standard error of the mean (σ_x̄) equals:
σ × n
σ / n
σ / √n
σ² / n
2. A population is strongly right-skewed. With n = 40, the sampling distribution of x̄ is approximately:
Also right-skewed
Normal (by CLT)
Uniform
Bimodal
3. If you quadruple the sample size from n=25 to n=100, the standard error:
Halves (÷2)
Quarters (÷4)
Doubles (×2)
Stays the same
Check Answers