Skewness and dispersion are two statistical concepts that help in understanding data distribution or the spread and behavior of data points.
Skewness addresses the asymmetry or lack thereof in the distribution of data points, providing an indication of how skewed or symmetric a dataset is. Dispersion encompasses a range of measures that elucidate the extent to which data points are scattered or concentrated around a central tendency, portraying the variability and spread within a dataset.
Let us look at the characteristics that differentiate these two concept.
What is Dispersion?
In statistics, dispersion is the extent to which a distribution is stretched or squeezed. Common examples of measures of statistical dispersion are the variance, standard deviation, and interquartile range. For instance, when the variance of data in a set is large, the data is widely scattered. On the other hand, when the variance is small, the data in the set is clustered.
In statistics, the measures of dispersion help to interpret the variability of data i.e. to know how much homogenous or heterogeneous the data is. In simple terms, it shows how squeezed or scattered the variable is.
There are two main types of dispersion methods in statistics which are:
- Absolute Measure of Dispersion
- Relative Measure of Dispersion
An absolute measure of dispersion contains the same unit as the original data set. The absolute dispersion method expresses the variations in terms of the average of deviations of observations like standard or means deviations. It includes range, standard deviation, quartile deviation, etc.
The relative measures of dispersion are used to compare the distribution of two or more data sets. This measure compares values without units. Common relative dispersion methods include:
- Co-efficient of Range
- Co-efficient of Variation
- Co-efficient of Standard Deviation
- Co-efficient of Quartile Deviation
- Co-efficient of Mean Deviation
What is 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.
Skewness gives the direction of the outliers if it is right-skewed, most of the outliers are present on the right side of the distribution while if it is left-skewed, most of the outliers will present on the left side of the distribution. But the important thing to keep in mind it doesn’t tell about the number of outliers.
Skewness vs Dispersion: Key Differences
|Nature||Shows the spread of values from the central value||Shows whether series is symmetrical or asymmetrical.|
|Basis||It depend upon the averages of second order.||Depends upon the averages of first and second order.|
|Relationship with moment||Based on all three moments||Based on first and third moment only.|
|Variability||Study of the Variability||Study of concentration in lower and higher variables.|
|Diagrammatic presentation||Cannot be presented by means of diagrams & graphs.||Skewness can be presented by diagram.|
|Inference||All the measures of dispersion are positive.||Coefficient of skewness can be positive or negative.|
- Dispersion defines a spectrum that extends or extends a distribution, whereas skewness is a measure of the asymmetry of a random variable around the average of statistical distribution.
- Dispersion based on a certain average is determined, whereas skewness based on the medium, median, and mode are determined.
- Both measures of dispersion and skewness are descriptive measures and coefficient of skewness gives an indication to the shape of the distribution.
- Dispersion shows the important distribution from the main value, whereas skewness shows symmetrical or asymmetrical series.
- In dispersion, all the measures are positive, whereas, in skewness, all the measures are negative.
- 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
- Dispersion is also useful for the testing of average reliability, whereas skewness is useful in the study of the financial market, which includes vast numbers of information such as asset returns, inventory values, etc., is highly useful.