Simulating by sampling with replacement (bootstrapping)
Consider trying to give a confidence interval for the mean from [attachment:before.jpg Raw positive skewed data.]
One way to achieve this is to bootstrap (Efron and Tibshirani, 1993) and repeatedly sample a large number of times. Sampling 500 times, taking the means of these samples and then repeating this 49 more times creates 50 sample [attachment:after.jpg bootstrapped means.]
This distribution is symmetric and, therefore, by taking the 5% and 95% percentiles we obtain a 95% Confidence interval for the sample mean.
_Reference_
Efron and Tibshirani (1993)