 # Variable Definition  View Notes

## What is a Variable?

Mathematics consists of an algebraic expression that has a combination of constants, variables, coefficients and fundamental operations like addition, division, subtraction, and multiplication. Every single term constitutes the basis of algebra.

While studying Algebra, one will find an alphabet that is used to portray an unknown number. The alphabet represents value. Variable quantities might be changed by the given mathematical problem. The most generally used variables are x, y, and z. In simpler terms, a variable stands as a symbol for an unknown number whose value is not given.

For example,

x + 8 = 16; “x” here acts as a variable.

The value of the “x” variable can easily be found by working out the problem. Here the value of “x” will be 8 that means x=8.

The term variable is also used in subjects like statistics. Variables in statistics are referred to as data items. The variable represents numbers/characteristics which could be measured. Example, age, income, sex, capital expenditure, etc. are few such variable examples available in statistics.

## Different Types of Variables

There are many types of variables but we will discuss roughly three different variables. Different Types of Variables in Maths:

### 1. Dependent Variables:

A dependent variable is the type of variable that generally tends to depend on the values of other numbers or variables. Precisely, a dependent variable often acts as the output of a function.

The change in the value of an independent variable affects the change of the dependent variable as it is dependent on it. That is so because the value of the dependent variable depends on what is put into the function.

Example: y= 5 + 3x

Here, y acts as a dependent variable and thus is called so. The value of y depends completely on the function 5 + 3x

### 2. Independent Variable:

An Independent variable is the type of variable that generally tends to not depend on the value functions of other variables or numbers. It is also known as the input of a function. The dependent variable depends on this variable i.e the independent variable for its value.

Example: x = 3y + 4z

Here, x refers to a dependent variable

y and z act as the independent variables because y and z values do not get affected by other values.

## Types of Variable in Research

### Qualitative Variables:

Two variables differ in qualitative factors and quantitative factors. Qualitative variables are the variables that are used to express qualitative attributes namely hair colour, race, religion, social caste, gender, method payment, etc.

Qualitative variables are often known as Categorical Variables.

Example: There are two different categories in variable sex namely ‘male’ and ‘female’. As the variable values are expressed in different categories, it is referred to as a categorical variable.

1. What are the Two Different Cardinal Variables?

Ans. Categorical variables can be further divided and described as nominal variables and ordinal variables.

Ordinal variables generally refer to variables that can be logically ranked higher or ordered or even ranked lower than another but they don't need to establish numeric differences between each provided category.

For example, in the case of examination grades. (A, A+, B, B+, C, D, etc.,); in case of different sizes of clothes (extra small, small, medium, large, extra-large, double xl)

On the other hand, nominal variables generally refer to those variables that can neither be logically ordered, for example, religion and sex nor can it be ranked.

Qualitative variable characteristics generally are not measurable but they can be categorized, not to possess or even possess few of the characteristics.

Q2. What Do You Mean By Discrete and Continuous Variables?

Ans: Quantitative variables can be further divided into two more types namely discrete and continuous.

Variables like the number of children present in a household or the number of items in a box that are defective are known as discrete variables as the possible scores generally are discrete when measured on a scale.

Example: A family could consist of 6 children or 7 children and not have 6.85 children.

Other examples of such variables will be time required for finishing an examination or waiting in line for tickets all are examples of continuous variables. The time needed in the above-mentioned variables might be 1.88 minutes or it could even be 1.887403842 minutes.

Continuous variables are variables that require an infinite number of intermediate values along with a specified interval. Even extreme closeness of the variable will not affect the precise measurement and the third observation which is supposed to fall between one and two.

Few examples of both continuous and discrete variables:

• The number of truck accidents in the last 15 years.

• Sugar levels of the human body.

• The number of paintings sold at the workshop.

• Weight or height of different human bodies.

• The number of milk packets sold over a specific period.

Q3. What are the Different Levels of an Independent Variable? Briefly Discuss Background Variables.

Ans. When the person performing the experiment treatment along with a control treatment, when compared to the independent variable, has roughly two levels namely experimental and control.

For example, an experiment was supposed to compare three types of diets and the independent variable i.e types of diets would have three levels.

Speaking generally, the number of levels of an independent variable is the same as the number of experimental conditions.

Background variables play a vital role in everyone’s everyday lives. In roughly all studies, there is a necessity to collect information like sex, age, educational attainment, marital status, socioeconomic status, place of birth, religion, etc.

All these variables are known as background variables. These variables are mostly related to other independent variables and are thus influenced indirectly by the problem.

Thus they are referred to as background variables. Background variables are often very important in a study. If it plays an important role in the study, it should properly be measured. The number of variables background however should be tried and kept as few as possible for the economy.

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