** 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**

In statistics, the dispersion is the variation of a random variable or its probability distribution. It is a measure of how far the data points lie from the central value. To express this quantitatively, measures of dispersion are used in descriptive statistic.

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.

Pearson’s first skewness coffeicent = (mean – mode) / (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?**

Dispersion concerns about the range over which the data points are distributed, and the skewness concerns the symmetry of the distribution.

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.