CLT central limit theorem demo

Type or paste the unknown
population data:
(Data distribution generator can make any amount of data from various distributions)
      N=
      μ=
      σ=

sample size n:       √n=
#samples:

The sampling distribution of the mean:
Sample means x̄i

Mean of the sample means μx̄= ∑x̄i/#samples:   will approach the population μ.

Standard deviation of the sample means (AKA standard error [of the mean], SEM) σx̄=   will approach the population σ/√n.
    σx̄·√n= ≈σ

The sampling distribution of the standard deviation:
Sample standard deviations si

Mean of the sample standard deviations =∑si/#samples:

Statistics, frequency distribution, histogram 


Standard normal pop. μ=0. σ=1  N=100,000
10,000 samples of n=10 --> σx̄≈ .32
10,000 samples of n=100 --> σx̄≈ .1

Uniform pop. [0,100]  μ=50. σ=29  N=100,000
10,000 samples of n=10 --> σx̄≈ 9.2  range~20-80
10,000 samples of n=100 --> σx̄≈ 2.9 range~40-60

Exponential pop. λ=.1  μ=10. σ=10  N=100,000
10,000 samples of n=10 --> σx̄≈ 3.16  range~2-27
10,000 samples of n=100 --> σx̄≈ 1 range~7-14