$[$P$-3\mathrm{.}57]$: Perform experimental analysis to test the hypothesis that Python$$s sorted method runs in O$($n log n$)$ time on average. Please write me the code in python.

Note: You would have a list that would initially start from size $2,$ with random numbers in it$,$ pass it to the sort method and calculate the time that method took to sort the list. Increase the list size by $1$ with appended random number and time how long would the method sorts, repeat the process until list size is large. As size would be increasing, the time it takes to sort is also increasing, show that method is run as O$($n log n$)$ time on average by plotting a graph.