The speed of a train is an independent variable that determines how long a trip takes (dependent variable).
Variables are, in the field of mathematics, symbols that appear in a function , a formula , a proposition or an algorithm . Their main characteristic is that they have the ability to adopt different values .
When the value of a magnitude depends exclusively on the value of another magnitude, a mathematical function is established. This second magnitude, which determines the value of the first, is called the independent variable . On the other hand, the magnitude whose value depends on the other acts as a dependent variable .
An etymological analysis
It is important that we know that this term is made up of two words that, etymologically speaking, come from Latin:
-Variable derives from “variabilis”, which means that something can change its appearance and is made up of two different parts: the verb “variare” (to change appearance) and the suffix “-able”, which is used to indicate possibility.
-Independiente, on the other hand, is the result of the union of three Latin components: the prefix “in-”, which indicates negation; the verb “dependere”, which can be translated as “to be under the will of another”; and the suffix “-nte”, which is used to record the “agent”.
Data of interest about the independent variables
In addition to all the information that we have provided about the aforementioned independent variable, it is necessary to know other data of interest such as these:
-When used in the field of mathematics or statistics, it is represented by the “x”.
-In your case, it always develops on what is known as the abscissa axis.
-Also in some sectors it is referred to as a manipulated variable.
-It is characterized because it is assigned values that are arbitrary.
-Within these are the control variables, which modify the rest of the independent variables and that can alter a result due to bias.
The price paid for potatoes is a variable dependent on the number of kilograms purchased, which is the independent variable.
An example
Take the case of a man who must go from his home to his workplace, 10 kilometers away. The time it takes you to cover the journey will depend on the speed at which you are moving. In this way, we can establish a function where speed is the independent variable that determines the duration of the trip (dependent variable).
If this person decides to travel on a train that moves at a constant speed of 60 kilometers per hour , it will take him 10 minutes to reach his workplace. On the other hand, if you prefer to go to work on a bus that travels at 45 kilometers per hour , the duration of the trip will be just over 13 minutes .
As can be seen in the example, the independent variable of this function is speed , while travel time is the dependent variable. How long the trip takes depends on the speed: the speed, in this function, depends on itself.
It is important to note that this is a theoretical example that helps understand what an independent variable is. In real life, the speed of a means of transport is not usually constant and even varies throughout the day.
Other cases of independent variables
Simple examples of what an independent variable is are these:
-The price we pay for some potatoes, the dependent variable, will depend on the number of kilos of potatoes we buy, the independent variable.
-The cost of a taxi trip, the dependent variable, is given by the length of the trip, the independent variable.