What are dependent variables? Give an example.

Dependent variables are, as you might guess, variables that depend on certain conditions. An independent variable is a variable whose value can be freely changed. A variable is dependent if its value is adjusted as a direct consequence of a change in the independent variable.

For example, consider a square with side length x. Then its perimeter is 4 times the side length,

P = 4x

and its area is the square of the side length,

A = x ²

If x = 1, then P = 4 and A = 1. If x = 2, then P = 8 and A = 4. And so on. If we treat x as the independent variable, then P and A are dependent variables that depend on the value of x.

But you can also go the other way and express x as functions of P or A, making x a dependent variable that depends on the values of P or A. For example, solving for x in terms of P gives

P = 4x   ===>   x = P/4

Then if P = 4, we have x = 8. If P = 16, then x = 1. And so on. You can think of A in the same way.

You can even go one step further and express the area A as a function of the perimeter P :

P = 4x   ===>   x = P/4

Then

A = x ² = (P/4)² = P ²/16

So in this case, P is the independent variable upon which the dependent variable A depends. If P = 4, then A = 1. If P = 8, then A = 4. etc

In a scientific study, "independent variable" is associated with some quantity or measurement that you control, and the "dependent variable" is the quantity or measurement that you take in response to a change in the independent variable. The meaning of either is the same, but actual studies typically don't involve simple equations like the ones I use as examples here.