How to Use Probability Distribution to Understand Your Data Critically

Posted on Posted in Data Analytics
Is there any basis why probability distribution has to be talked about? What are its uses in understanding data? Can it show a sense of relevance according to one’s needs? These are some of the questions that one has to ask in studying probability statistics.
Taking into consideration all of the questions above, it is better to have an overview of the use of histogram as this can directly answer them. Try to look at this histogram:

 

 

This histogram summarizes certain data.  It must be taken note of that the primary function of histogram is to show a summary of variation in measured data. One might wonder whether a certain curve comes from a distribution or from any other mathematical computation that approximates the histogram. The fundamental idea here is that this histogram fits to a probability function. The curve made is an attempt to show probability distribution. Technical know-how of probability is the core concept and even one of the critical building blocks in getting to more advanced analytics and machine learning.
Going deeper, it is better to understand some of the basic concepts:
DISCRETE DISTRIBUTION
  1. Random Variables
Its values are subject to changes because it depends on randomness. In other words, a chance process is a determinant factor in the the selection of samples. It can take on many possible numbers or items. For example, in chosing five (5) representatives of a group with ten (10) members, random picking of names written on a rolled pieces of papers. In this, everybody is given an equal chance to represent the group, but not all can be chosen. However, even after the extremities are determined, in this case the five representatives, there is still no definite description as to who or what the outcome is. This is because there is no exact definition of the outcome as the latter is just a represetative of the whole. In the example given, it is true that five representative are chosen, but they do not necessarily carry the exact definition of the the other five (5) members not chosen. In other words, the description that can be provided is probability-state base.
By definition, discrete probability describes the probability of occurrence of each value of a discrete random variable. Bear in mind that discrete random variable always has countable values. This is there reason why the best way to present this is through a table. Colloquially speaking, this is based on chances. For example, in tossing a coin, there is fifty percent (50%) chance of getting a tail. Understanding the unsaid, there is also 50 percent (50%) chance of getting a tail. This is called binary distribution.

 

 

If there are 6 six persons who are tasked to roll a dice to get number 6, each one of them has 1/6 chance of getting number 6. What is disctinct about this kind is that when you add all the values of all probabilites, you can always arrrive at one. Consider the table below:

 

 

CONTINUOUS DISTRIBUTION

Actually, there is the same concept as in the discrete disctribution. The possible outcomes are in the x-axis and the probabilities are in the y-axis.However, unlike discrete contribution wherein you can find countable values, in continuous distribution, the description is based on continuous random variables. A continuous random variable is infinite and uncountable. Using the same example as used above, it is not possible to use this kind of distribution in tossing a coin. The reason is that one cannot arrive at having half tail or half head. There is really no possibility that its  continuous random variable can equal any value. In other words, the probability that X is exactly equal to some value is always zero. This is the basic idea behind it.
Let’s take the following example that describes the height of American women (ages30-39):

 

 

Here, the probability that all of these women can have the same height is zero. One can make a calculation that women can reach a height less than fifty-nine (59) inches or less than seventy-one (71) inches, but the probability that all of them can reach the same height is zero.