Basic Tools Of Mathematics And statistics In Economics

Modern economists consider the use and help of fundamental mathematical 

tools to discuss the relationship of various quantities in economics very fruitful.

In view of the importance of such relationships we study the following concepts:

Variables

Generally the quantities which change their values are known as "Variables".

It can be well defined as under:

"A variable is a magnitude which is measureable and taken of different values"

According to Prof. Kooros "A variable is a symbol which during a discussion may

assume different values or a set of admissible values".

E.T. Dowling defines variable as under:

"A variable ranges over a set of possible values within a given problem".

In normal life Time, Temperature, Speed of a vehicle are regarded as variables.

In economics there are many quantities which also change their values e.g 

Income, Consumption, Saving , Investment, Price, Demand, Supply, Utility etc.

In mathematics some letters of alphabet(x,y,z) are used to represent Variables. 

But in economics generally  first capital letter of the quantity is used for variable 

e.g P for price, C for consumption, S for saving, I for investment, Utility for utility

etc.

However sometimes specific symbols may be used e.g Yorkshire for National 

Income, M for Imports, X for exports etc.

Continues Variable 

A continuous variable is a variable can take on any score or value within a 

measurement scale. Continues Variables are height, temperature, time,

income, weight and distance.

In this graph we take time along x axis and distance on y axis. Distance is the  measure of path that is traveled. Therefore this graph represents continuous
data.

Discontinues variable

A discontinuous variable is a value that can have two or more possible values

but has a limited number of values. Thus the data set is missing those values,
making it a discontinuous data set.

Constant variable 

The value of constant variable are "known"and "fixed". According to E.T. Dowling 

"A constant is a quantity that doesn't change in a given period"

The numbers in any equation are constants for instance  4x+2=6. In this equation 4,

2,6 are constants while x is a variable.

Parameters 

There are certain quantities whose values keep on changing in real life but for 

specific purposes:

These are assume to "remain the same". These quantities are known as parameters. 

Functions

Some variables are inter-related withe each other when one variable (y), depends

on other variable  (x) then y =f (x). Variable "y" is a function of variable "x" expresses 

a rleationship between two variables (x,y) such that for each value of x there exists 

one and only one value of y.

Equations

An equation expresses the equality between two algebraic expressions.

More simply we can say that "An equation is a statement that two algebraic

expressions are equal". The sign of equation is (=). An algebraic expression 

is a combination of Numbers,Letters with + or - signs.

Every part with + or - signs is called  "Term" for example  (¡) 2x+4 = 4x-6

(¡¡) x+y = 5 are equations.

In equation no (¡) 2x+4 is an algebraic expression having two terms:

(¡) 2x (¡¡)+4. The two algebraic expressions are called L.H.S and 

R.H.S (left and right hand side)of the equation. 

One Side of the equation my be zero e.g 4x-2 = 0. According to "Terms"

algebraic expressions are as under:

(¡) Binomial 

An algebraic expression with only two terms e.g 3x-5 , 2x+6

(¡) Trinomial

An algebraic expression having three terms

(¡¡¡) polynomial

The algebraic expressions having four or more than four terms.