Statistics – Variables:
Suppose we are conducting an experiment to count the marks of students in a class based on a surprise test. We want to know how many students can attempt the test based on memory. We get a list of marks which is varying its value among the students. This item marks is known as variable which is studied in a sample or population.
It can also be defined as below:
- A statistical variable is each of the characteristics or qualities that any individual of a population possess and can be any number, characteristic or quantity which can be counted.
- A variable is a data item, where the value varies between data units in a population and can change value over time.
Variables can be further categorized as below:
Qualitative variables can be values that are names or labels. Lets have a look at this table:
| Scale | Properties | Examples | Qualitative / Quantitative | |
| Nominal Operations: =, ≠≠ | There will be a difference however order will not be changed. | Maruthi = 1 Hyundai = 2 Volkswagen=3 Audi = 4 BMW = 5 Other = 6 | Qualitative | |
| Ordinal Operations: =, ≠≠, <, > | There will be a difference and direction of the difference will be indicated (less than or more than) | Food taste Agree = 1 | Qualitative | |
| Binary Operations: =, ≠≠ | There will be a difference as it has only 2 values True/False or 0/1 | Sun rises in the east? True | Qualitative |
Quantitative variables are numerical measurable quantity.
Example:
when we say population of a city, we are thinking about the number of people in the city which is a measurable attribute (quantity)of the city. Therefore, population is a quantitative variable.
We can further classify Quantitative variables as discrete or continuous. If a variable holds any value between its minimum value and its maximum value, it can be called as continuous variable; otherwise, a discrete variable.
Some of these examples will differentiate discrete and continuous variables:
- Suppose the fire department mandates that all fire fighters must weigh between 75 and 90 kilos. The weight of a fire fighter would be an example of a continuous variable; since a fire fighter’s weight could take on any value between 75.0 and 90.0 kilos.
- Suppose we flip a coin to count the number of heads. The number of heads can hold any integer value between 0 and +∞. But, We cannot get 2.3 heads. So, the number of heads must be a discrete variable.
In an experiment, a variable can be divided into two types:
- Independent(explanatory/predictor) variable,
- Dependent(response) variable .
A variable which influence changes in the response variable is known as predictor variable and is often known as the independent variable. Independent variable can be random or non random. An independent variable is mostly an input or cause variable. It is tested to see if it is the cause. The explanatory variable can be either categorical data or quantitative data.
In an experimental study, response variable is used as a measure of an outcome . It represents the output or effect and is tested to see if it is the effect. Response variable is dependent on the explanatory variable and is also known as dependent variable, explained variable, outcome variable, experimental variable. It is called as dependent variable which depends on the independent variable.
Suppose we held a survey to know how stress rate affects heart rate in human kind. The dependent variable is the heart rate which varies with stress so, the independent variable is stress.