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.
The followings steps denotes some of the concepts for modeling the world.
Convert the given problem into statistics modeling.
Solve the statistics problem.
Interpret the result for the real situation.
If need arises, modify the model.
The concepts of statistics modeling the world can be expressed through the following figure.
Suppose the present population of a city is 100000 and we want to find its population, say after 10 years.
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.