Lab 01 / Sampling
Why averages settle down
What changes when you average a skewed population?
Draw repeated samples from a right-skewed synthetic population and watch the distribution of their means change with sample size. Change one control at a time, then open the values under the chart before interpreting the picture.
View the values behind this chart
Loading the deterministic simulation...
SEEDInterpret the result
The paired guide explains the mechanism, assumptions, and cases where this display should not be generalized.
What this display answers
The bars are a distribution of averages, not a distribution of individual observations. Each bar counts averages from a new sample of the selected size.
As sample size increases, the spread of those averages should approach the source standard deviation divided by the square root of the sample size. The center should remain close to the source mean even though the source itself is strongly skewed.
What to notice
- Set the sample size to 1 first. The histogram preserves the long right tail of the source model.
- Increase the sample size while keeping the repetitions fixed. The histogram narrows and becomes more symmetric, but no individual observation has changed its distribution.
- Use New draw. Small visual bumps change; the general relationship should remain.
The model behind it
The source is a log-normal teaching model. Every sample is independent, the log-scale parameters stay fixed, and the displayed source mean is calculated analytically.
The comparison line uses the exact model mean. The observed spread uses only the simulated sample means, so it moves slightly when the seed changes.
Where the result stops
This does not show that every sample mean is normal, or that a sample size of 30 is a universal threshold.
Dependence, changing populations, very heavy tails, and selection bias can invalidate the simple picture.