1.1

1+2*(3+4)
## [1] 15
4^3+3^(2+1)
## [1] 91
sqrt((4+3)*(2+1))
## [1] 4.582576
((1+2)/(3+4))^2
## [1] 0.1836735

1.2

\((2+3)-4\)

\(2+(3\times4)\)

\((2 \div 3) \div 4\)

\(2^{(3^4)}\)

1.3

(1+2*3^4)/(5/6-7)
## [1] -26.43243

1.4

(0.25-0.2)/sqrt(0.2*(1-0.2)/100)
## [1] 1.25

1.5

x1<-2; x2<-3; x3<-4; x4<-5
x <- x1*x2*x3*x4
# show the result
x
## [1] 120

1.6

data("rivers")
rivers
##   [1]  735  320  325  392  524  450 1459  135  465  600  330  336  280  315
##  [15]  870  906  202  329  290 1000  600  505 1450  840 1243  890  350  407
##  [29]  286  280  525  720  390  250  327  230  265  850  210  630  260  230
##  [43]  360  730  600  306  390  420  291  710  340  217  281  352  259  250
##  [57]  470  680  570  350  300  560  900  625  332 2348 1171 3710 2315 2533
##  [71]  780  280  410  460  260  255  431  350  760  618  338  981 1306  500
##  [85]  696  605  250  411 1054  735  233  435  490  310  460  383  375 1270
##  [99]  545  445 1885  380  300  380  377  425  276  210  800  420  350  360
## [113]  538 1100 1205  314  237  610  360  540 1038  424  310  300  444  301
## [127]  268  620  215  652  900  525  246  360  529  500  720  270  430  671
## [141] 1770

1.7

# Load the related packages
library(MASS)
library(HistData)
library(lattice)
library(survival)
library(Formula)
library(ggplot2)
library(Hmisc)
library(UsingR)
data("exec.pay")
exec.pay
##   [1]  136   74    8   38   46   43    9    9   12   11   20    9   95   34
##  [15]    7   14   39   12   29   21   60   35   17   36   29  162   88   31
##  [29]    6  135   13   20    9   14   28   42   10   35    2   16   28   42
##  [43]  142   33  134   23   34   16   13  167    9   22   39   28   30   22
##  [57]   14    9   25  106   32   30   89   89   47   17   26 1231    6  103
##  [71]   48   24   11   19   13   29   20   45    3   33   41    7   11   10
##  [85]   22   36    7   19   41   40   10   15   93   67   29   25   91   38
##  [99] 2510    5   32   65    0   13   27   16   21    6    0   28    8   13
## [113]   71   36   11  106   37   41   13  900   38   24   15   27   12   12
## [127]   22   40   49   22  118   48   10    1   36  155    9   34   29   12
## [141]    0   28   21   32   18   52   29   13  199   40   11   51   45   43
## [155]   31    5   18   15   25    9   18   13   58   22   40   34   16   31
## [169]   27   15   23   49   60   28   74   42   24   17    9   61   20   23
## [183]   26   31  167   19   14   13  146  283   12   53   26   16   29   51
## [197]   15   22   27

1.8

mean(exec.pay); min(exec.pay); max(exec.pay)
## [1] 59.88945
## [1] 0
## [1] 2510

1.9

mean(exec.pay); mean(exec.pay, trim = 0.1)
## [1] 59.88945
## [1] 29.96894

1.10

data("Orange")
# return the names of three variables
names(Orange)
## [1] "Tree"          "age"           "circumference"

1.11

mean(Orange$age)
## [1] 922.1429

1.12

max(Orange$circumference)
## [1] 214

1.18

x = c(1, 3, 5, 7, 9)
y = c(2, 3, 5, 7, 11, 13)
x+1
## [1]  2  4  6  8 10
y*2
## [1]  4  6 10 14 22 26
length(x); length(y)
## [1] 5
## [1] 6
x+y
## Warning in x + y: longer object length is not a multiple of shorter object
## length
## [1]  3  6 10 14 20 14
sum(x>5); sum(x[x>5])
## [1] 2
## [1] 16
sum(x>5|x<3)
## [1] 3
y[3]
## [1] 5
y[-3]
## [1]  2  3  7 11 13
y[x]   
## [1]  2  5 11 NA NA
y[y>=7]
## [1]  7 11 13

1.19 Consider the following “inequalities.” Can you determine how the comparisons are being done?