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In probability theory and statistics, skewness is a measure of the asymmetry of the probability distribution of a real-valued random variable about its mean. The skewness value can be positive or negative, or even undefined. The qualitative interpretation of the skew is complicated. For a unimodal distribution, negative skew indicates that the ''tail'' on the left side of the probability density function is longer or fatter than the right side – it does not distinguish these shapes. Conversely, positive skew indicates that the tail on the right side is longer or fatter than the left side. In cases where one tail is long but the other tail is fat, skewness does not obey a simple rule. For example, a zero value indicates that the tails on both sides of the mean balance out, which is the case for a symmetric distribution, but is also true for an asymmetric distribution where the asymmetries even out, such as one tail being long but thin, and the other being short but fat. Further, in multimodal distributions and discrete distributions, skewness is also difficult to interpret. Importantly, the skewness does not determine the relationship of mean and median. ==Introduction== Consider the two distributions in the figure just below. Within each graph, the bars on the right side of the distribution taper differently than the bars on the left side. These tapering sides are called ''tails'', and they provide a visual means for determining which of the two kinds of skewness a distribution has: #': The left tail is longer; the mass of the distribution is concentrated on the right of the figure. The distribution is said to be ''left-skewed'', ''left-tailed'', or ''skewed to the left''.〔Susan Dean, Barbara Illowsky ("Descriptive Statistics: Skewness and the Mean, Median, and Mode" ), Connexions website〕 #': The right tail is longer; the mass of the distribution is concentrated on the left of the figure. The distribution is said to be ''right-skewed'', ''right-tailed'', or ''skewed to the right''.〔 Skewness in a data series may be observed not only graphically but by simple inspection of the values. For instance, consider the numeric sequence (49, 50, 51), whose values are evenly distributed around a central value of (50). We can transform this sequence into a negatively skewed distribution by adding a value far below the mean, as in e.g. (40, 49, 50, 51). Similarly, we can make the sequence positively skewed by adding a value far above the mean, as in e.g. (49, 50, 51, 60). 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「skewness」の詳細全文を読む スポンサード リンク
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