(of a function)
Let f be a function that is continuous on the closed interval [a, b]. The mean value of f over the interval [a, b] is equal to
The mean value ȳ has the property that the area under the curve y=f(x) between x=a and x=b is equal to the area under the horizontal line y=ȳ between x=a and x=b, which is the area of a rectangle with width b−a and height ȳ.
For example, the function may represent the temperature measured at a certain place over a period of 24 hours. The mean value gives what may be considered an ‘average’ value for the temperature over that period.