Statistics modeling the world:

The statistics modeling consists of translating a real-world problem into mathematical problem, solving it and interpreting the solution in the language of real world. The process of constructing statistics models is called statistics model. A statistics modeling is a mathematical relation that describes some real life situation. The statistics modeling are used to solve many real-life situations.

 

 

Concepts for modeling the world:

 

The followings steps denotes some of the concepts for modeling the world.

Step 1:

Convert the given problem into statistics modeling.

Step 2:

Solve the statistics problem.

Step 3:

Interpret the result for the real situation.

Step 4:

If need arises, modify the model.

The concepts of statistics modeling the world can be expressed through the following figure.


 

Example problems for statistics modeling in real world:

 

Suppose the present population of a city is 100000 and we want to find its population, say after 10 years.

Solution:

Let p (t) be the population in a certain year t.

Let B (t) be the number of births and D (t) be the number of deaths between the years t and t + 1. Then,

P (t + 1) = P (t) + B (t) – D (t) `=>` (1)

Let B (t) / p (t) = b and D (t) / p (t) = d. then,

P (t + 1) = p (t) + b p (t) – d p (t)

 `=>` p (t + 1) = (1 + b - d) p (t) `=>` (2)

Putting t = 0 in (2),

We get p (1) = (1 + b - d) p (0)  0 `=>` (3)

Putting t = 1 in (2),

We get p (2) = (1 + b - d) p (1)

                   = (1 + b - d)2 p (0) (using 3)

Thus p(2) = (1 + b - d)2 p (0).

  

Continuing in this way, we get:

P (t) = (1 + b - d)t p (0) for t = 0, 1, 2,….

 `=>` p (t) = p (0) * rt,

Where (1 + b - d) = r.

Suppose it is given that p (0) = 100000, b = 0.02 and d = 0.01.

Then, p (10) = (1.01)10 * 100000

[Let (1.01)10 = 1.104622125 be given]

                      = (1.104622125 * 100000) = 1104622.125.

Since we cannot have the number of persons in decimal fraction, the above result is not valid.

So, we take the population as 1104622 approximately.