The manipulated variable is your independent variable. This gets plotted along the x-axis on a graph, and your dependent variable gets plotted along the y axis.
Example- think of a velocity-time graph (physics), or a dose-response graph (pharmacology). The variable you are able to control (like time or dose) is your manipulated variable, and the variable whose value is contingent on how you manipulate the first is your dependent variable (drug response etc.)
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