Measures of Dispersion

Before diving into Measures of Dispersion, it is better to get a brief introduction to statistics. Statistics is the part of science that helps many in developing and studying the methods for collecting, analyzing, interpreting, and presenting the data. Statistics is also known as the highly interdisciplinary domain. Statistics have proved to be beneficial in the field of science. If you level it up, its methods are prevalent among Data Science techniques. Statistics play a vital role in almost every field. From mathematics to Data Science, statistics are found to be very helpful in finding new methods to solve problems. Research work has given rise to various statistical approaches, which are now advantages in analyzing and manipulating data.

The field of statistics has two fundamental ideas: uncertainty and variation. You may have seen many situations in your life where the results are uncertain. Similarly, many of the solutions to scientific problems are also uncertain. Sometimes your solution is uncertain because the result is not yet determined. In other cases, uncertainty occurs because we are unaware of the already present solution. Probability is the Mathematical concept that talks about certainty and uncertainty, and it plays a significant role in predicting situations. If you repeat the same measuring process, the result will likely change.

Coming to the Dispersion in Statistics, it is the way of describing how to spread out the data set. Dispersion indicates the data being dispersed, stretched, or spread out into different categories. Dispersion helps you find the distributed value for your particular variable. Summarizing Dispersion in Statistics numeric data may vary if there is vary in any instance of average value assumption. Dispersion helps categorize the data sets based on their Dispersion criteria like ranging, standard deviation, and variance. It allows one to determine the quality of the data in an objectively quantifiable manner. It is seen that the Measures of Dispersion almost has the same unit as the quantity being measured. 

Several Measures of Dispersion allow you to get valuable insights from the data. They are:

• Range

• Variance

• Standard Deviation

• Skewness

• IQR

Measures of Dispersion are divided into two main categories, which offer to measure the diverse nature of data. The two categories are:

• Absolute Measure of Dispersion

• Relative Measure of Dispersion

Absolute Measure of Dispersion

Absolute Measure of Dispersion showcases the same unit as the initial data set. It is expressed in terms of the average of the Dispersion quantities like Mean or Standard Deviation. Types of Absolute Measure of Dispersion include:

• Range : The Range is considered the simplest form of Dispersion that provides the difference between the largest to the smallest value of the data variability.

• Mean : Mean allows you to find the average. To find the average of your outcomes, add all of them and divide them by the total number of terms.

• Variance : Variance can be found by finding the sum of the squared distances of each term in the mean distribution and dividing this sum by the total number of terms present.

• Standard Deviation : The square root of the variance found will provide you with the Standard Deviation. Hence, it is clear that to find the Standard Deviation of any data, you must first calculate its variance.

• Quartile : It divides the list of data into Quartiles.

• Quartile Deviation : It is the measure of the difference between the upper and lower Quartile of the data. This Measure of Dispersion is also known as the Interquartile Range. 

• Mean Deviation : Average Deviation or the Mean Deviation is found by computing the mean or median of the data. It is also represented as the arithmetic deviation of the different data that follows the central tendency.

Relative Measures of Dispersion

These relative Measures of Dispersion are unitless. It is mostly utilized to draw comparisons for the distribution of multiple data sets. Relative Measures of Dispersion are the same as the Absolute Measure of Dispersion, and the only difference is the measuring quantity. Relative Measures of Dispersion are the calculation of the coefficients of the Dispersions. Here, two data series are compared, but they differ widely in their average. It comes into the picture when two different series of coefficients are compared. 

• Co-efficient of Range : It is the ratio of the difference between the largest and lowest terms of the distribution to the sum of these terms of the distribution.

• Co-efficient of Standard Deviation : It is the ratio of the Standard Deviation to the Mean of the distribution of the terms.

• Co-efficient of Quartile Deviation : It is the ratio of the difference between the upper and lower quartile to their sum.

• Co-efficient of Mean Deviation : On computing the Mean or Median of the data, you will get the coefficient of Median Deviation.

The knowledge of these Dispersions is considered vital as they allow you to diversify the data and understand how it is spread out and maintained. You can find many Measures of Dispersion examples to help you understand these concepts better. You will understand when and where these Measures of Dispersion have importance in the data set value. To understand Measures of Dispersion better, enroll in Great Learning’s free Measures of Dispersion course and get in-depth knowledge of all the essential concepts. Complete all the modules introduced in the course successfully to earn free Measures of Dispersion certificate, enhance your resume, and grab better job opportunities. Enroll Today!