When is the area under the line is equal to the mean

[Fahad Mirza]

Hi everyone,

I recently generated an area chart which connects the points using a straight line and noticed that the area under the line as a percentage of the total area is equaling the calculated mean. Is this a coincidence or am I doing something wrong in the calculation. For the calculation of area i am using integ with the option of trapezoid.

The raw values themselves range from 0 to 100.

I am not sure how to share a data example for this but just thought i ask in what conditions can this happen.

Thanks!

[Nick Cox]

The mean is the area under the quantile function, a k a the inverse cumulative distribution function.

[Fahad Mirza]

Nick Cox thank you!