Other Definitions
skewness (dict)
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SkewnessIn probability theory and statistics, skewness is a measure of the asymmetry of the probability distribution of a real-valued random variable. Roughly speaking, a distribution has positive skew (right-skewed) if the higher tail is longer and negative skew (left-skewed) if the lower tail is longer; getting these the wrong way round is a common error. Skewness, the third standardized moment, is defined as μ3 / σ3, where μ3 is the third moment about the mean and σ is the standard deviation. The skewness of a random variable X is sometimes denoted SkewX. For a sample of N values the sample skewness is Σi(xi − μ)3 / Nσ3, where xi is the ith value and μ is the mean. If Y is the sum of n independent random variables, all with the same distribution as X, then it can be shown that SkewY = SkewX / √n. Given samples from a population, the equation for population skewness above is a biased estimator of the population skewness. An unbiased estimator of skewness is -
\left(\frac{\sum_{i=1}^n \left( x_i - \bar{x} \right)^3}{n\sigma^3}\right) where is the sample standard deviation and is the sample mean. Pearson Skewness Coefficients Karl Pearson suggested two simpler calculations as a measure of skewness: though there is no guarantee that these will be the same sign as each other or as the ordinary definition of skewness. See also External links
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