Distribution of the averages
0 samplesaverages you drewa perfect normal curve
Draw some samples to begin. Each one takes a sample from your population and drops its average onto the chart.
The normal curve shows up everywhere in statistics, even when what you measured is nowhere near a bell. Here is why. Pick a lop-sided population, then draw samples and watch the averages build one anyway.
Every bar is one sample's average. Individually the values are lop-sided, but their averages pile up in the middle and thin out at the edges, forming a bell. That is the Central Limit Theorem: the distribution of sample means is close to normal even when the population is not.
The bell always sits over the true population average. Turn up n and it gets narrower, because bigger samples estimate the mean more precisely. Its spread is the population spread divided by the square root of n, the standard error, and it is why larger studies give tighter estimates.