Independent and Dependent Variables

Bivariate data is numerical data that consists of two variables organized into pairs of values.
It compares two variables.
Non-bivariate data provides only one numerical data point; an example is favorite ice cream flavor and the number of students who like it.

Bivariate data highlights the relationship between a reason (cause) and its result (effect).
Example: Continuous rainy season (cause) leads to an increase in umbrella sales (effect).
Example: Increased price of goods (cause) leads to a decrease in the number of grocery items you can buy (effect).

The independent variable is the variable that, when changed, affects the other variable.
It represents the "cause" in a cause-and-effect relationship.
Example: Continuous rainy season is the independent variable that causes an increase in umbrella sales.

The dependent variable is the variable whose value depends on the independent variable.
It represents the "effect" in a cause-and-effect relationship.
Example: Exam score is dependent on the time (in hours) spent studying.
- 4 hours spent studying results in a score of 84.
- 3 hours spent studying results in a score of 80.
- 6 hours spent studying results in a score of 95.
- 2 hours spent studying results in a score of 76.
- 5 hours spent studying results in a score of 89.

The number of grocery items you can buy (dependent variable) is affected by the price of goods (independent variable).

The independent variable is placed on the x-axis (horizontal axis).
The dependent variable is placed on the y-axis (vertical axis).
Example: Graphing time spent studying (independent variable) vs. score on exam (dependent variable).

Independent Variable:
- It does not depend on any other variables.
- It is located on the horizontal (x) axis.
Dependent Variable:
- It depends on the value of the independent variable.
- It is located on the vertical (y) axis.

Consider scenarios where input and output are at play to identify independent and dependent variables.