This histogram shows sampling from a Uniform distribution.

There is a lot of variation between the histogram shown in the display and the smooth "ideal" distribution. The histogram will always be "jaggy." The "ideal" is the Uniform Distribution shown in books - but it never will be seen in an actual sampling situation. What does it mean to say that the sampling results will "approach" the theoretical distribution as the number of samples increases?

There always will be jagginess - and it doesn't go away as the number of samples increases. It actually gets larger in absolute terms. But it gets smaller and smaller as a proportion of the number of samples as the number of samples increases. So if we "zoom out" with respect to the vertical (count of observations) scale and fit more and more samples in the same height histogram, then the jagginess (variation from the true smooth Uniform Distribution) will get smaller as a proportion of the height.

Specifically, here the "zoom out" factor is 9x, and so the variation seen in the histogram is expected to decrease to one third of what it was before. (Why? Hint: consider the square root of the sample size.)

	(Panic Stop) After sampling stops:
	Total Obs.