### Lack of Symmetry

Skewness is the lack of symmetry (lack of normality) in a probability distribution. The skewness is usually quantified by the index as given below

$$s = \frac{\mu_3}{\mu_2^{3/2}}$$

where $\mu_2$ and $\mu_3$ are the second and third moments about the mean.

This index formula described above takes the value zero for a symmetrical distribution. A distribution is positively skewed when it has a longer and thin tail to the right. A distribution is negatively skewed when it has a longer thin tail to the left.

Any distribution is said to be skewed when the data points cluster more toward one side of the scale than the other. Creating such a curve that is not symmetrical.

*Skewed Data*

*Skewed Data*

The two general rules for Skewed Data are

- If the mean is less than the median, the data are skewed to the left, and
- If the mean is greater than the median, the data are skewed to the right.

Therefore, if the mean is much greater than the median the data are probably skewed to the right.

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