How Maths, Probability, and Statistics are related?

1. Mathematics:

It is the base for every technical subject. Be it any domain, at least we are going to perform basic mathematical operations like addition, subtraction etc.

Therefore, the story starts with Maths. We use tools and techniques defined in Mathematics to solve problems of any other domain namely Science, Statistics, Probability, Artificial Intelligence, Data Science and so on.

2. Probability:

As Harvey J. Motulsky mentioned in Intuitive Biostatistics “Probability calculations go from general to specific, from population to sample, and from model to data.”

It is the field where the rules and formulas are already defined, and in the real world we pick one specific problem statement, use the formula and come up with the result.

Example: When an unbiased/fair dice is rolled, what is the probability that it shows “3”

As we already know in general, an unbiased dice has 6 different faces (1, 2, 3, 4, 5, 6). And all the 6 faces have equal chance of occurrence.

To solve the given specific problem, we use above general knowledge and can find out that probability of showing 3 will be 1 / 6

 
3. Statistics:

Motulsky further says that “Statistics help you extrapolate from a particular set of data (your sample) to make a more general conclusion (about the population). Statistical cal-culations go from specific to general, from sample to population, from data to model”

We start with something small and then extrapolate this to make a general inference.

Example: What is the average weight of all the people in India?

It is hard to weigh each person in India to get the result, hence we will focus on a smaller set and after analyzing this smaller set, we will draw conclusions for the whole population in India.

Pick one set of 1,00,000 people (You may consider a set of 50,000 or 2,00,000 or any other number)

• from various states and cities,
• from various age groups,
• from various genders,
• from various professions.
  

Now after weighing these 1,00,000 people (which is our sample), we can conclude about the average weight of whole population of India.

In Short, Probability has its own rules (the general rules) and using these general rules we can solve specific problems.

In Statistics, we collect one sample set (which is “Specific” data) and using inferential statistics we generalize it for the whole population.

Note: We will be learning soon about How to derive a population statistics when a sample statistics is given