What is the difference in meaning between a "variable" and a "parameter" in a given equation?
Solution 1:
The difference in mathematical statistics is very clear-cut. Suppose you have a set of data which you believe behaves according to a quadratic law
y = a x2 + b + c.
So you have observed lots of pairs of values (x,y)—with errors—and you are trying to estimate a, b and c. Then x and y are called variables and a, b, and c are called parameters.
In general mathematical terminology, the definitions are essentially the same. For functions, the inputs and outputs are variables, and other values in the definition of the function that might possibly change are called parameters. Here, however, you are not trying to estimate the parameters from observed values of the variables, so the definitions are somewhat fuzzier; you could treat the same object as a variable and as a parameter in two different sections of the same mathematical paper.
Note that the above definition does not apply to parametric equations, where the variables in a function are defined in terms of a parameter which does not appear in the function.
Solution 2:
Note: This answer is with regards to programming, not mathematics.
Variable is a term used generically refer to a storage location, usually in memory, holding data for a program. (Sources: C# language definition, Wikipedia). I like this explanation from about.com:
Imagine a very large warehouse with lots of storage bays, tables, shelves, special rooms etc. These are all places where you can store something. Lets imagine we have a crate of beer in the warehouse. Where exactly is it located?
The variable is the location of the crate, given a symbolic name like "beerLocation" so you can easily reference it.
Of course, variable in the literal sense means "able to vary", so in some contexts this can be used as a means of differentiating between data that can be altered (variable) and data that is fixed (constant).
A parameter is a special type of variable, used in reference to data passed to functions/subroutines/macros. Sources: MSDN doc, Wikipedia. There is some subtle difference between parameters and arguments, but they are often used interchangeably.
Solution 3:
Variable refers to it has a changing values or context . A parameter is a special kind of variable, used in a subroutine to refer to one of the pieces of data provided as input to the subroutine.These pieces of data are called arguments. An ordered list of parameters is usually included in the definition of a subroutine, so that, each time the subroutine is called, its arguments for that call can be assigned to the corresponding parameters.