1. Population
Skewed population
Start by taking one sample slowly. Watch how a random sample produces one sample mean.
Population values
Selected in current sample
Population values are commute times in minutes. Most are moderate, but a few long commutes pull the distribution to the right.
2. Current Sample
One random sample is shown here, then its average is calculated.
Waiting for sample
Take a sample to begin.
3. Sampling Distribution of x̄
Each sample mean drops onto the dot plot. Repeated samples build the sampling distribution.
One sample → one dot
Sample means
4. Summary
As more sample means are collected, the center and spread of the sampling distribution become easier to see.
Live summary
Population mean (μ)
--
Population SD (σ)
--
Mean of sample means
--
SD of sample means
--
Samples taken
0
Mean of the sampling distribution
μx̄ = μ
μx̄ = μ = --
μx̄ = --
Standard deviation of the sampling distribution
σx̄ = σ / √n
σx̄ = -- / √--
σx̄ = --
At first, the sampling distribution will look rough. After more samples, the pattern becomes clearer.