**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.

**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.

**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) * r^{t},

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.