Final answer:
In statistics, variables or events that are not associated with each other are called independent variables, thus the correct option is d.
Explanation:
In statistics, variables or events that are not associated with each other are called independent variables. This means that the value of one variable does not affect or depend on the value of the other variable. In other words, there is no relationship or connection between the two variables. This is in contrast to dependent variables, where the value of one variable is affected or influenced by the value of the other variable.
To further understand the concept of independent variables, let's take a look at an example. Let's say we are conducting a study to determine if there is a relationship between studying and grades. In this case, studying is the independent variable and grades are the dependent variable. This is because the amount of time spent studying does not depend on the grades, but rather, the grades are affected by the amount of time spent studying.
Another way to think about independent variables is to consider them as the cause and dependent variables as the effect. The independent variable is the one that is manipulated or changed, while the dependent variable is the one that is measured or observed.
In mathematical terms, independent variables are represented by x and dependent variables by y. For example, in the equation y = 2x + 3, x is the independent variable and y is the dependent variable. This equation shows that the value of y depends on the value of x, and the relationship between the two is a linear one.
In some cases, there may also be multiple independent variables that can affect the dependent variable. These are called multiple independent variables. For example, if we are studying the factors that influence job satisfaction, we may have multiple independent variables such as salary, work-life balance, and job security.
In conclusion, independent variables are variables or events that are not associated with each other, meaning that changes in one do not affect the other. They are represented by x in equations and are the cause of the dependent variable. Understanding the concept of independent variables is crucial in statistical analysis as it helps in determining the relationship between variables and making accurate predictions, thus the correct option is d.