An extreme portion of a distribution, where the relative frequency becomes low either to the left or to the right, is called a tail.
A distribution is said to be symmetric if the relative frequency (or probability) is the same the same distance either side of its centre, m. Mathematically, the distribution of X-m is then the same as the distribution of m-X. The mean and median of a symmetric distribution are equal.
The most important symmetric distribution is the normal distribution, which is unimodal and therefore is symmetric about the mode. For symmetric unimodal distributions, the mean, median and mode are all the same.
An asymmetric frequency distribution is skewed to the left if the lower tail is longer than the upper tail, and skewed to the right if the upper tail is longer than the lower tail. Distributions of positive-valued random variables values are often skewed right.
An example of positive skewness
An example of negative skewness
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