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A numerical value is any number. It is known. A numerical value is fixed. A numerical value is a constant. A numerical value could be final solution for a variable.
Example : A number like five, ten , half, a quarter etc. Any special numerical expression like 2+2, 5+10^2 , a dozen , a crore, etc.
A variabe is any quantity assumed. We assume that x is the number that has to be added t0 5 to get thirteen. So we solve x+ 5 = 13 . So we can assume any value for the unknown x of the equation , it is a variable. But x = 8 is the only one value for which x+8 = 13 holds true. So now the solution x = 8 is a constant. The set of all values that could be assumed form the variable x set . But a particular value ( here the solution of x, i.e , 8) is a solution to x+8 = 13 which is a constant .
You assign variables to unknown quantities or quantities that change in value depending on some other factor. Lets say you have a problem where you want to know the number of people in a bus. That number is dependent on the starting number of people and the number of people that exit or board the bus. So you would assign a variable to the total number of people. Continuing this problem, if we know there are 25 people on the bus, and at every stop 3 people board, and 5 people exit.
The total number (x) depends on the number of stops (y) and we could write that as:
x = 25 + 3y - 5y
Simplify to: x = 25 + 2y
Here x refers to the changing total number of people on the bus. And y refers to the number of stops. 25 is a set starting value. 2 is the net number of people that board the bus at a stop.
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