Measures of Dispersion - Meaning, Types

Dispersion refers to the degree to which data can deviate from the average value, aiding in our understanding of data distribution. Various measures of dispersion offer insights into the variability of data, revealing whether the data is consistent or diverse. These measures help us determine if the data is widely dispersed or tightly clustered.

A Measure of Dispersion encompasses numerical representations that illustrate the extent of data scattering, revealing different facets of data distribution across various parameters.

Measures of Dispersion Meaning

Within the field of statistics, measures of dispersion serve the crucial purpose of deciphering the diversity within data, essentially telling us whether the data is uniform or diverse. In simpler terms, they reveal how tightly or widely spread the variable is.

These dispersion measures are usually presented in units similar to the ones used in the dataset. Range, Variance, Standard Deviation, Skewness, and IQR are among the diverse metrics providing crucial insights, enabling a more profound comprehension of the data's traits.

Types of Measures of Dispersion

The Measure of Dispersion in Statistics is separated into two major areas and provides methods for assessing the variety of data. We can readily categorize them by determining whether or not they include units. we may split the data into two categories:

• Absolute Dispersion Measures
• Relative Dispersion Measures

Absolute Dispersion Measures

Absolute Measures of Dispersion are those that use the same units as the original dataset. They are expressed in terms of average dispersion values like Standard or Mean deviation and can be denominated in units such as Rupees, Centimeters, Marks, kilograms, or other relevant units depending on the context.

There are several types of Absolute Measures of Dispersion in Statistics:

Range:

The range is the easiest measure of dispersion that is calculated as the difference between the largest and the smallest value in the data set. Such as in the dataset, 1, 2, 3, 4, 5, 6, 7, the range is (7-1) = 6.

Mean (μ):

The average of the data is referred to as the mean, which is found by adding up all the terms and dividing by the total of terms. For example, in the dataset 1, 2, 3, 4, 5, 6, 7, 8, the mean is [(1 + 2 + 3 + 4 + 5 + 6 + 7 + 8) /

Variance (σ²):

The extent that each data point is from the mean is quantified by variance. The total squared deviations between each data point and the mean, divided by the total number of data points.

Standard Deviation:

The square root of variation is the standard deviation. It is widely used, particularly as one of the most effective dispersion measures.

Quartile:

The Quartiles divide the data into quarters, and Quartile Deviation (or interquartile range) is the difference between the upper and the lower quartiles. It's calculated as Q3 - Q1.

Mean Deviation:

Mean deviation, commonly known as average deviation, is computed using either the Mean or Median of the data. It stands for the arithmetic difference between the mean and individual data points.

Relative Dispersion Measures

Relative Measures of Dispersion in statistics are numerical values that lack specific units. They are employed to compare the distribution of multiple datasets.

There are various types of Relative Measures of Dispersion, primarily calculated through coefficients that facilitate the comparison of series

Coefficient of Range:

This ratio compares the difference between the largest and smallest terms of a distribution to the sum of these values. It's represented as (Largest Value - Smallest Value) / (Largest Value + Smallest Value).

Coefficient of Variation:

This coefficient, expressed as a percentage, enables the comparison of data in terms of consistency. It is calculated as the ratio of the standard deviation (σ) to the mean (X), represented as (σ / X) * 100.

Coefficient of Standard Deviation:

This ratio involves the standard deviation divided by the mean of the distribution terms. The formula is ( √( X – X1)) / (N - 1), where X is the standard deviation, X1 is the deviation, and N is the total number of terms.

Coefficient of Quartile Deviation:

This ratio compares the difference between the upper quartile (Q3) and lower quartile (Q1) to their sum. The formula is (Q3 - Q1) / (Q3 + Q1).

Coefficient of Mean Deviation:

This coefficient is computed using either the mean or median of the data. Mean Deviation using Mean is calculated as the sum of the absolute differences between each data point and the mean, divided by the total number of terms. Mean Deviation using Median follows a similar process but uses the median instead of the mean.

Formulas for Measures of Dispersion

The following table provide the general formulae used to determine various measures of dispersion: