Part of developing different computational tools is doing an analysis of the computational time of algorithms. This can be done a couple of different ways in R. You can either use system.time() or a package called microbenchmark.

Let's look at the computational time of the sort() algorithm, in particular the quicksort method. The quicksort algorithm was developed by Tony Hoarse in 1959. It is a particularly fast sorting algorithm that has an average computation time of nlog(n)n for a list of size n

First we create a random vector of size 1000000 by x<-rnorm(1000000)

Implementing the code, system.time(sort(x,method="quick"))

10 times we have the following table of computational times for the quick sort algorithm

Measurement	Elapsed time (secs)
1	0.088
2	0.109
3	0.093
4	0.083
5	0.086
6	0.088
7	0.088
8	0.110
9	0.085
10	0.104

Problems:

1. What is the population of the study? What is the sample?
2. Give the five number summary of the data.
3. The microbenchmark library automatically runs a code snippet multiple times. Use the code summary(microbenchmark(sort(x,method="quick"),times=10,unit="s")) to find the 5 number summary of computational times using microbenchmark.
4. Draw boxplots of both the system.time() and microbenchmark summaries on a single axis.