1. Storethevalues − 20, − 15, − 5, 8, 12, 9, 2, 23, 19 in the R variable x and use the R command sum to verify that the sum of the values is 33.
x <- c(-20,-15,-5,8,12,9,2,23,19)
sum(x)
## [1] 33
  1. For the data in Exercise 1, verify that the average is 3.67 using the R command mean
mean(x)
## [1] 3.666667
  1. What R commands can be used to compute an average without using the R command mean ?
sum(x)/length(x)
## [1] 3.666667
  1. In Exercise 1, use R to sum the positive values ignoring the negative values.
sum(x[x>0])
## [1] 73
  1. In Exercise1, use the which command to get the average of the values ignoring the largest value.
mean(x[x<max(x)])
## [1] 1.25
  1. If the data in Exercise1 are stored in the variable x , speculate about the values corresponding to x[abs(x)>=8 & x<8] . Verify your speculation using this R command.

Speculation: This command will return values of x that have an absolute value greater than or equal to 8 and a value less than 8. Namely, -20 and -15

x[abs(x)>=8 & x<8]
## [1] -20 -15
  1. You record your commute time to work for 10 days, in minutes, and get 23, 18, 29, 22, 24, 27, 28, 19, 28, 23. Use R to determine the average, the shortest time, and the longest time.
t <- c(23,18,29,22,24,27,28,19,28,23)
mean(t)
## [1] 24.1
min(t)
## [1] 18
max(t)
## [1] 29
  1. Verify that the commands y=c(2,4,8) z=c(1,5,2) 2*y return the values 4, 8, 16. Also, verify that the R command y+z returns 3, 9, 10 and that the command y-2 returns 0,2,6.
y=c(2,4,8)
z=c(1,5,2)
2*y
## [1]  4  8 16
y+z
## [1]  3  9 10
y-2
## [1] 0 2 6
  1. Let x = c(1, 8, 2, 6, 3, 8, 5, 5, 5, 5) . Use R to compute the average using the sum and length commands. Next, use a single command to subtract the value 4 from each value stored in x. Finally, find the difference between the largest and smallest values stored in x. (This difference is called the range.) You can use the max and min functions or the range function.
x = c(1, 8, 2, 6, 3, 8, 5, 5, 5, 5)
x-4
##  [1] -3  4 -2  2 -1  4  1  1  1  1
max(x)-min(x)
## [1] 7
  1. For the data in Exercise 9, use R to subtract the average from each value, and then sum the results.
x-mean(x)
##  [1] -3.8  3.2 -2.8  1.2 -1.8  3.2  0.2  0.2  0.2  0.2
sum(x-mean(x))
## [1] 1.776357e-15