Difference Between Dispersion and Skewness

Dispersion vs Skewness

In statistics and probability theory, often the variation in the distributions has to be expressed in a quantitative manner for the purposes of comparison. Dispersion and Skewness are two statistical concepts where the shape of the distribution is presented in a quantitative scale.

More about Dispersion

在统计中，分散是随机变量或其概率分布的变化。这是数据点与中心价值相距多远的衡量标准。为了定量地表达这一问题，分散度的度量用于描述性统计量。

Variance, Standard Deviation, and Inter-quartile range are the most commonly used measures of dispersion.

If the data values have a certain unit, due to the scale, the measures of dispersion may also have the same units. Interdecile range, Range, mean difference, median absolute deviation, average absolute deviation, and distance standard deviation are measures of dispersion with units.

In contrast, there are measures of dispersion which has no units, i.e dimensionless. Variance, Coefficient of variation, Quartile coefficient of dispersion, and Relative mean difference are measures of dispersion with no units.

Dispersion in a system can be originated from errors, such as instrumental and observational errors. Also, random variations in the sample itself can cause variations. It is important to have a quantitative idea about the variation in data before making other conclusions from the data set.

More about Skewness

In statistics, skewness is a measure of asymmetry of the probability distributions. Skewness can be positive or negative, or in some cases non-existent. It can also be considered as a measure of offset from the normal distribution.

If the skewness is positive, then the bulk of the data points is centred to the left of the curve and the right tail is longer. If the skewness is negative, the bulk of the data points is centred towards the right of the curve and the left tail is rather long. If the skewness is zero, then the population is normally distributed.

In a normal distribution, that is when the curve is symmetric, the mean, median, and mode have the same value. If the skewness is not zero, this property does not hold, and the mean, mode, and median may have different values.

Pearson’s first and second coefficients of skewness are commonly used for determining the skewness of the distributions.

皮尔森的第一个偏态coffeicent =(平均-模式) / (standard deviation)

Pearson’s second skewness coffeicent = 3(mean – mode) / (satndard deviation)

In more sensitive cases, adjusted Fisher-Pearson standardized moment coefficient is used.

G = {n / (n-1)(n-2)} ∑ⁿ_i=1((y-ӯ)/s)³

What is the difference between Dispersion and Skewness?

分散有关数据点分布的范围的问题，偏度涉及分布的对称性。

Both measures of dispersion and skewness are descriptive measures and coefficient of skewness gives an indication to the shape of the distribution.

Measures of dispersion are used to understand the range of the data points and offset from the mean while skewness is used for understanding the tendency for the variation of data points into a certain direction.