Description
1. The vectors state.name, state.area, and state.region are pre-loaded in R and contain US state names, area (in square miles), and region respectively.
(a) Identify the data type for state.name, state.area, and state.region.
(b) What is the longest state name (including spaces)? How long is it?
(c) Compute the average area of the states which contain the word “New” at the start
of the state name. Use the function substr().
(d) Use the function table() to determine how many states are in each region. Use
the function kable() to include the table in your solutions. (Notes: you will need
the R package knitr to be able to use kable(). See the RMarkdown example in
the Assignments folder on Blackboard for an example.)
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2. Perfect numbers are those where the sum of the proper divisors (i.e., divisors other than
the number itself) add up to the number. For example, 6 is a perfect number because
its divisors, 1, 2, and 3, when summed, equal 6.
(a) The following code was written to find the first 2 perfect numbers: 6 and 28;
however, there are some errors in the code and the programmer forgot to add
comments for readability. Debug and add comments to the following:
num.perfect <- 2
count <- 0
iter <- 2
while(count <= num.perfect){
divisor <- 1
for(i 2:(iter-1)){
if(iter%%i==0) divisor <- c(divisor, i)
} # end for loop
if(sum(divisor)=iter){
print(paste(iter, " is a perfect number", sep="")
count <- count + 1
} # end if
iter <- iter + 1
} # end while loop
(b) Use the function date() at the start and at the end of your amended code. Then
compute how long the program approximately takes to run (you can do this subtraction by hand). Find the run time when you set num.perfect to 1, 2, 3, and 4.
Create a table of your results (Note: use the first table format in the RMarkdown
Example file in the Assignments folder on Blackboard) . What are the first four
perfect numbers?
(c) Let x <- 1:4 and define y to be the vector of run times. Plot y vs x using the code
below. Is the relationship between the discovery of perfect numbers and run times
on your computer linear? Justify your answer.
plot(x, y, pch=20, type="b",
xlab="number of perfect numbers discovered",
ylab="cumulative length of time (in seconds)",
main="Cumulative Run Times to Discover Perfect Numbers",
las=TRUE)
SDGB 7844, C.H. Nagaraja Page 2 of 3
3. The geometric mean of a numeric vector x is computed as follows:
x˜ =
Yn
i=1
xi
!1/n
.
(a) Using a for loop, write code to compute the geometric mean of the numeric vector
x < −c(4, 67, 3). Make sure your code (i) removes any NA values and (ii) prints an
error message if there are any non-positive values in x.
(b) Test your code on the following cases and show the output: (i) {NA, 4, 67, 3}, (ii)
{0, NA, 6}, (iii) {67, 3, ∞}, and (iv) {−∞, 67, 3}.
SDGB 7844, C.H. Nagaraja Page 3 of 3
