QQ Plot Challenge
Is the sample reasonably consistent with normality?
Changing the sample size generates a new sample from the same underlying population. Try both very small and very large samples.
The plot compares the observed sample quantiles with theoretical quantiles from a normal distribution.
Is this sample reasonably consistent with a normal distribution?
Generating distribution:
Advanced: from samples to sampling distributions
Keep the population from this question fixed, but now imagine repeating the experiment many times. Change the sample size and watch what happens to the mean.
Your challenge: how large does the sample need to be before the sampling distribution of the mean looks reasonably like the distribution expected under the Central Limit Theorem?
Central Limit Theorem
The grey bars are simulated sample means. The dashed curve is the normal sampling distribution expected from the CLT, when the usual finite-variance conditions are satisfied.
Law of Large Numbers
This is one long sequence of observations from the same population. The line shows the running mean as more observations are added. When the population mean exists, compare it with the horizontal reference line.
A QQ plot does not prove that a population is normal. The question is whether departures from the normal reference pattern are large enough to be visually convincing. With very small samples, strong departures can also be difficult to see.