This may be a very basic math but I am stuck in a type of inference. Below is an illustration of a function say $y = f(t)$. This is shown continuous, but we have a sample data with a 10 sec interval. The unit is $W/m^2$. We are interested in average value of this per unit time, say per minute or per hour.
When I take naively the average between $(t_1,t_2)$, I would only get the avearage $\bar{y}$ within the time period $(t_1,t_2)$. Extending this inference further, at any point of time $t$ within $(t_1,t_2)$, the expected $y$ would be $\bar{y}$.
To convert to kWh/m2, we need the average of $y$ per unit time, say per hour. How do we get to that from here? As per my understanding, $\bar{y}$ is instantaneous expected value of y at time t. But then what would be next step here for average $y$ per hour, say $\bar{y_1}$
The area under the curve is $$\int\limits_{t_1}^{t_2} f(t)\, dt = \bar y (t_2 - t_1)$$
If $t$ is measured in hours $(h)$, and $f(t)$ and $\bar y$ are measured in $W/m^2$, then the integral has units $Wh/m^2$.
If $t$ is measured in seconds $(s)$, and $f(t)$ and $\bar y$ are measured in $W/m^2$, then the integral has units $Ws/m^2$.
To get from a numerical answer with units $Ws/m^2$ to $Wh/m^2$, divide by $60^2=3600$.
To get from a numerical answer with units $Wh/m^2$ to $kWh/m^2$, divide by $1000$.