I want to create a simple boxplot from 1D data, which doesn't seem to be supported by the default Insert → Charts. There is a histogram gadget but I haven't seen any boxplot gadgets.
Do I have to make my own gadget using google charts API?
The closest thing to a Boxplot Chart is a Candlestick Chart.
You could calculate all the data needed to plot a box chart: The Five Number Summary and plot each serie individually. Apparently, the width of the box isn't important.
In Google Apps Script, the box charts are un-supported.
I've created an example file for you: Box Plot
You can use the addon g(Math) it is under statistical display and will create a box and whisker chart as below.