Skewness describes the asymmetry of a distribution. A skewed distribution therefore has one tail longer than the other.
A positively skewed distribution has a longer tail to the right:
A negatively skewed distribution has a longer tail to the left:
A distribution with no skew (e.g. a normal distribution) is symmetrical:
In a perfectly symmetrical, non-skewed, distribution the mean, median and mode are equal. As distributions become more skewed the difference between these different measures of central tendency gets larger.
Positively skewed distributions are more common than negatively skewed ones.
A coefficient of skewness for a sample is calculated by StatsDirect as:
- where xi is a sample observation, x bar is the sample mean and n is the sample size.
Skewed distributions can sometimes be "normalized" by transformation.