variable in mathematics vs variable in statistics I was wondering about the difference between a variable in mathematics and a variable in statistics.
In mathematics, a variable is defined as a symbol that can represent different values.
Example: In the expression $x + 3$, $x$ is a variable. This means that $x$ is an empty symbol that doesn't mean anything. However, $x$ can be made to equal different numbers. When we say $x = 2$, we are asserting that $x$ symbolizes $2$. Consequently, $x + 3 = 5$.
In statistics, a variable is defined as a characteristic. I understand a characteristic as a label that we assign to a quantity. I understand a quantity as a number or a number with a unit.
Example: 3 feet is a quantity. Height is a label that we give to this quantity. Height is a characteristic. Height is also a variable.
In my mind, these definitions for variables seem different. Am I thinking about them wrong?

Here's the Merriam-Webster definition of variable:

1a: a quantity that may assume any one of a set of values
b: a symbol representing a variable

We can see that "variable" in mathematics and "variable" in statistics, in the way described in your question, actually correspond to different part of this definition. Height is a variable, in the sense that it is a quantity that can take several possible values. $x$ is a symbol representing a variable, and of course that variable could very well be a height.
But just to be clear, both parts of the definition are used in math and stats. In algebra, $x$ can be just a symbol, but in a particular problem it can represent a specific quantity. Similarly, in statistics, instead of talking of a specific variable such as height, we may want to be as general as possible and therefore represent it by a symbol such as $x$.
