Independent & Dependent Variables
Identify independent and dependent variables for NSW Year 12 Mathematics Standard 1 (NESA outcome MST-12-S1-06). The independent variable is the one that is chosen, changed or does the influencing; the dependent variable is the response that gets measured.
You will sort the variables in a bivariate dataset, check your choice with the “depends on” test, put the independent variable on the horizontal axis and the dependent one on the vertical axis, and decide when one may really cause a change in the other — such as a plant’s growth depending on the water it gets.
Theory
In bivariate data the independent variable is the one that is chosen, changed or does the influencing; the dependent variable is the response that is measured. This Year 12 Standard 1 (NSW) guide shows how to tell them apart with the “depends on” test and why the independent variable goes across and the dependent variable goes up.
The independent (explanatory) variable is the one that is set, chosen or changed, or that can influence the other. It goes on the horizontal axis.
The dependent (response) variable is the outcome that is measured; it responds to the other. It goes on the vertical axis.
Test with the sentence “dependent depends on independent”, e.g. the plant’s height depends on the amount of water. If neither variable is set, choose the one that can influence the other.
There is no calculation here — use the sentence test and the axis rule:
How to identify the independent and dependent variables
- Ask which variable is set, chosen or changed — that is the independent variable.
- Identify the response that is measured — that is the dependent variable.
- Check with the sentence “dependent depends on independent”.
- Place the independent variable across and the dependent variable up.
Decide which one the baker sets and which one is measured.
| \(\text{baking time is set}\) | \(\Rightarrow\) | \(\text{independent}\) |
| \(\text{moisture is measured}\) | \(\Rightarrow\) | \(\text{dependent}\) |
| \(\text{check: moisture depends on time}\) | \(\) | \(\checkmark\) |
Independent: baking time; dependent: moisture left in the loaf.
Choose the variable that can influence the other.
| \(\text{age}\) | \(\Rightarrow\) | \(\text{can change blood pressure}\) |
| \(\text{blood pressure}\) | \(\Rightarrow\) | \(\text{cannot change age}\) |
Age is the independent variable, and blood pressure is the dependent variable.
The subscribers respond to the price.
| \(\text{(i) subscribers respond}\) | \(\Rightarrow\) | \(\text{dependent}\) |
| \(\text{(ii) price is set}\) | \(\Rightarrow\) | \(\text{horizontal axis}\) |
(i) The number of new subscribers. (ii) The horizontal axis. (iii) The number of new subscribers depends on the price.
The vertical axis holds the dependent variable.
| \(B\ \text{on vertical axis}\) | \(\Rightarrow\) | \(\text{dependent}\) |
| \(p\uparrow\) | \(\Rightarrow\) | \(B\uparrow\ \text{(positive)}\) |
(i) The water bill is dependent (it depends on how many people use water). (ii) Positive. (A negative trend falls to the right, e.g. a car’s value as its age increases.)
Common pitfalls
Frequently asked questions
What is the difference between an independent and a dependent variable?
The independent variable is the one that is set, chosen or changed, or that does the influencing. The dependent variable is the response that is measured; it depends on the independent variable.
Which axis does the independent variable go on?
The independent variable always goes on the horizontal axis (across the bottom). The dependent variable goes on the vertical axis (up the side).
How do you work out which variable is dependent?
Test the sentence: the dependent variable depends on the independent variable. For example, plant growth depends on the amount of water, so growth is dependent and water is independent.
What if neither variable is controlled?
Choose the one that can influence the other. Temperature can change drink sales, but drink sales cannot change the temperature, so temperature is the independent variable.
Is time always the independent variable?
Time and age are usually independent, because nothing you measure can change how much time has passed or how old something is.