What is measures of dispersion in statistics
What is measures of dispersion in statistics

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What Is Measures Of Dispersion In Statistics 

A measure of dispersion is a numerical value which signifies the dispersion level of an entity or set of entities. A measure of dispersion can be either positive, negative, and is mostly used to show that some quantity is varying within different sets and not having an expected limit. In other words, it can give information about the extent to which one is dispersing values on an entity which consists of many independent entities. To illustrate dispersion, let’s say we have two types of people called Mark and Bob and want to know how much money will they make when starting up their own business. Let’s denote this as U and say that we also have another name, Z. This means that the total amount for both is equal to U, and so both values are equal to X, but then how much more is going to the left of the right side of the entity U.


Suppose you want to determine what kind of entity U is, it can either be either a person or a company, for example, if someone has a shoe shop, that shoe shop can then be a company, but the shoes that they are going to sell must have been manufactured by them; so this may be a company or a person. We need more than just to find out who this particular entity is because we need to find out why it was formed. The more dispersion there is, the less useful this entity will be. And so one-dimensional distribution would be very bad for us if we just calculated it without knowing anything else. There are more variables to consider, like whether it is a new start-up or something that already exists. Dispersion is very helpful in understanding the distribution when we are looking at multiple sub-types of some entity or an entity made up of several different sub-types like, suppose someone had a group of friends. If each individual were to say he has a friend then the aggregate figure could be higher than 50% of those he had a friend with. With Dispersion, we can find out if somebody has a relationship with his group of friends or not.


If there is any way to get information about the nature of dispersion, what is its objective? It can be seen as a way of measuring how the data is distributed without making assumptions of normality, non-Gaussianity, symmetry, etc. This is done by calculating and analyzing the mean, mode, standard deviation or mean absolute deviation. What is an appropriate measure?  the most natural measure of dispersion is mean absolute deviation or the square root of variance. The mean absolute deviation would give you the same type of results that will give you the same interpretation that other measures give; we can see if the data is symmetrical, the mean absolute deviation is the best way to interpret and get information about dispersion.