Figure 7.3 displays some clear features. The first, and perhaps most notable, is that almost all trace of the skewness of the original samples has gone – the distributions of the estimates based on the resampled data are almost symmetric around the mean of the original data. This is a first glimpse of what is known as the Central Limit Theorem, which says that the distribution of sample means tends towards the form of a normal distribution with increasing sample size, almost regardless of the shape of the original data distribution. This is an exceptional result, which we shall explore further
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