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Skewness

The normal distribution is symmetrical – small values are as likely as large values. The probability distribution for the normal distribution is symmetrical about the mean.

This is not the case for most distributions however. Most probability distributions are unsymmetrical and some are extremely so. The two graphs below are both positively skewed – the red one more so than the right one. The skew is always on the side of the tale. Both of the graphs below have long tales to the right. Notice the red distribution has a longer tail – it is more skewed.

The graphs below have negative skew – red one more so than the blue one.

The most common measure of skewness is given by

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