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data(murders)#q1:Use the $ operator to access the population size data and store it as the object pop. Then use the sort function to redefine pop so that it is sorted. Finally, use the [ operator to report the smallest population size.
pop<-murders$population
pop## [1] 4779736 710231 6392017 2915918 37253956 5029196 3574097 897934
## [9] 601723 19687653 9920000 1360301 1567582 12830632 6483802 3046355
## [17] 2853118 4339367 4533372 1328361 5773552 6547629 9883640 5303925
## [25] 2967297 5988927 989415 1826341 2700551 1316470 8791894 2059179
## [33] 19378102 9535483 672591 11536504 3751351 3831074 12702379 1052567
## [41] 4625364 814180 6346105 25145561 2763885 625741 8001024 6724540
## [49] 1852994 5686986 563626sort(pop)## [1] 563626 601723 625741 672591 710231 814180 897934 989415
## [9] 1052567 1316470 1328361 1360301 1567582 1826341 1852994 2059179
## [17] 2700551 2763885 2853118 2915918 2967297 3046355 3574097 3751351
## [25] 3831074 4339367 4533372 4625364 4779736 5029196 5303925 5686986
## [33] 5773552 5988927 6346105 6392017 6483802 6547629 6724540 8001024
## [41] 8791894 9535483 9883640 9920000 11536504 12702379 12830632 19378102
## [49] 19687653 25145561 37253956murders$population[which.min(pop)]## [1] 563626min(murders$population)## [1] 563626#q2:Now instead of the smallest population size, find the index of the entry with the smallest population size.
order(murders$population)## [1] 51 9 46 35 2 42 8 27 40 30 20 12 13 28 49 32 29 45 17 4 25 16 7 37 38
## [26] 18 19 41 1 6 24 50 21 26 43 3 15 22 48 47 31 34 23 11 36 39 14 33 10 44
## [51] 5#q3:We can actually perform the same operation as in the previous exercise using the function which.min. Write one line of code that does this.
murders$population[which.min(pop)]## [1] 563626#q4:Now we know how small the smallest state is and we know which row represents it. Which state is it? Define a variable states to be the state names from the murders data frame. Report the name of the state with the smallest population.
state<-murders$state
state## [1] "Alabama" "Alaska" "Arizona"
## [4] "Arkansas" "California" "Colorado"
## [7] "Connecticut" "Delaware" "District of Columbia"
## [10] "Florida" "Georgia" "Hawaii"
## [13] "Idaho" "Illinois" "Indiana"
## [16] "Iowa" "Kansas" "Kentucky"
## [19] "Louisiana" "Maine" "Maryland"
## [22] "Massachusetts" "Michigan" "Minnesota"
## [25] "Mississippi" "Missouri" "Montana"
## [28] "Nebraska" "Nevada" "New Hampshire"
## [31] "New Jersey" "New Mexico" "New York"
## [34] "North Carolina" "North Dakota" "Ohio"
## [37] "Oklahoma" "Oregon" "Pennsylvania"
## [40] "Rhode Island" "South Carolina" "South Dakota"
## [43] "Tennessee" "Texas" "Utah"
## [46] "Vermont" "Virginia" "Washington"
## [49] "West Virginia" "Wisconsin" "Wyoming"murders$state[which.min(murders$population)]## [1] "Wyoming"#q5:You can create a data frame using the data.frame function.
temp <- c(35, 88, 42, 84, 81, 30)
city <- c("Beijing", "Lagos", "Paris", "Rio de Janeiro", "San Juan", "Toronto")
city_temps <- data.frame(name = city, temperature = temp)
city_temps## name temperature
## 1 Beijing 35
## 2 Lagos 88
## 3 Paris 42
## 4 Rio de Janeiro 84
## 5 San Juan 81
## 6 Toronto 30population<-murders$population
population## [1] 4779736 710231 6392017 2915918 37253956 5029196 3574097 897934
## [9] 601723 19687653 9920000 1360301 1567582 12830632 6483802 3046355
## [17] 2853118 4339367 4533372 1328361 5773552 6547629 9883640 5303925
## [25] 2967297 5988927 989415 1826341 2700551 1316470 8791894 2059179
## [33] 19378102 9535483 672591 11536504 3751351 3831074 12702379 1052567
## [41] 4625364 814180 6346105 25145561 2763885 625741 8001024 6724540
## [49] 1852994 5686986 563626states<-murders$state
states## [1] "Alabama" "Alaska" "Arizona"
## [4] "Arkansas" "California" "Colorado"
## [7] "Connecticut" "Delaware" "District of Columbia"
## [10] "Florida" "Georgia" "Hawaii"
## [13] "Idaho" "Illinois" "Indiana"
## [16] "Iowa" "Kansas" "Kentucky"
## [19] "Louisiana" "Maine" "Maryland"
## [22] "Massachusetts" "Michigan" "Minnesota"
## [25] "Mississippi" "Missouri" "Montana"
## [28] "Nebraska" "Nevada" "New Hampshire"
## [31] "New Jersey" "New Mexico" "New York"
## [34] "North Carolina" "North Dakota" "Ohio"
## [37] "Oklahoma" "Oregon" "Pennsylvania"
## [40] "Rhode Island" "South Carolina" "South Dakota"
## [43] "Tennessee" "Texas" "Utah"
## [46] "Vermont" "Virginia" "Washington"
## [49] "West Virginia" "Wisconsin" "Wyoming"ranks <- rank(murders$population)
ranks## [1] 29 5 36 20 51 30 23 7 2 49 44 12 13 47 37 22 19 26 27 11 33 38 43 31 21
## [26] 34 8 14 17 10 41 16 48 42 4 45 24 25 46 9 28 6 35 50 18 3 40 39 15 32
## [51] 1my_df <- data.frame(name=state, ranks)
my_df## name ranks
## 1 Alabama 29
## 2 Alaska 5
## 3 Arizona 36
## 4 Arkansas 20
## 5 California 51
## 6 Colorado 30
## 7 Connecticut 23
## 8 Delaware 7
## 9 District of Columbia 2
## 10 Florida 49
## 11 Georgia 44
## 12 Hawaii 12
## 13 Idaho 13
## 14 Illinois 47
## 15 Indiana 37
## 16 Iowa 22
## 17 Kansas 19
## 18 Kentucky 26
## 19 Louisiana 27
## 20 Maine 11
## 21 Maryland 33
## 22 Massachusetts 38
## 23 Michigan 43
## 24 Minnesota 31
## 25 Mississippi 21
## 26 Missouri 34
## 27 Montana 8
## 28 Nebraska 14
## 29 Nevada 17
## 30 New Hampshire 10
## 31 New Jersey 41
## 32 New Mexico 16
## 33 New York 48
## 34 North Carolina 42
## 35 North Dakota 4
## 36 Ohio 45
## 37 Oklahoma 24
## 38 Oregon 25
## 39 Pennsylvania 46
## 40 Rhode Island 9
## 41 South Carolina 28
## 42 South Dakota 6
## 43 Tennessee 35
## 44 Texas 50
## 45 Utah 18
## 46 Vermont 3
## 47 Virginia 40
## 48 Washington 39
## 49 West Virginia 15
## 50 Wisconsin 32
## 51 Wyoming 1#q6:Repeat the previous exercise, but this time order my_df so that the states are ordered from least populous to most populous. Hint: create an object ind that stores the indexes needed to order the population values. Then use the bracket operator [ to re-order each column in the data frame.
state<-(murders$population)
state## [1] 4779736 710231 6392017 2915918 37253956 5029196 3574097 897934
## [9] 601723 19687653 9920000 1360301 1567582 12830632 6483802 3046355
## [17] 2853118 4339367 4533372 1328361 5773552 6547629 9883640 5303925
## [25] 2967297 5988927 989415 1826341 2700551 1316470 8791894 2059179
## [33] 19378102 9535483 672591 11536504 3751351 3831074 12702379 1052567
## [41] 4625364 814180 6346105 25145561 2763885 625741 8001024 6724540
## [49] 1852994 5686986 563626rank<-rank(murders$population)
rank## [1] 29 5 36 20 51 30 23 7 2 49 44 12 13 47 37 22 19 26 27 11 33 38 43 31 21
## [26] 34 8 14 17 10 41 16 48 42 4 45 24 25 46 9 28 6 35 50 18 3 40 39 15 32
## [51] 1ind<-order(murders$population)
ind## [1] 51 9 46 35 2 42 8 27 40 30 20 12 13 28 49 32 29 45 17 4 25 16 7 37 38
## [26] 18 19 41 1 6 24 50 21 26 43 3 15 22 48 47 31 34 23 11 36 39 14 33 10 44
## [51] 5my_df<-data.frame(state=state[ind],rank=rank[ind])
my_df## state rank
## 1 563626 1
## 2 601723 2
## 3 625741 3
## 4 672591 4
## 5 710231 5
## 6 814180 6
## 7 897934 7
## 8 989415 8
## 9 1052567 9
## 10 1316470 10
## 11 1328361 11
## 12 1360301 12
## 13 1567582 13
## 14 1826341 14
## 15 1852994 15
## 16 2059179 16
## 17 2700551 17
## 18 2763885 18
## 19 2853118 19
## 20 2915918 20
## 21 2967297 21
## 22 3046355 22
## 23 3574097 23
## 24 3751351 24
## 25 3831074 25
## 26 4339367 26
## 27 4533372 27
## 28 4625364 28
## 29 4779736 29
## 30 5029196 30
## 31 5303925 31
## 32 5686986 32
## 33 5773552 33
## 34 5988927 34
## 35 6346105 35
## 36 6392017 36
## 37 6483802 37
## 38 6547629 38
## 39 6724540 39
## 40 8001024 40
## 41 8791894 41
## 42 9535483 42
## 43 9883640 43
## 44 9920000 44
## 45 11536504 45
## 46 12702379 46
## 47 12830632 47
## 48 19378102 48
## 49 19687653 49
## 50 25145561 50
## 51 37253956 51#q7:he na_example vector represents a series of counts
data("na_example")
str(na_example)## int [1:1000] 2 1 3 2 1 3 1 4 3 2 ...#However, when we compute the average with the function mean, we obtain an NA:
mean(na_example)## [1] NAindex<-is.na(na_example)
index## [1] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE
## [13] FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [25] FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
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## [757] FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE TRUE FALSE
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## [877] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE
## [889] FALSE FALSE FALSE TRUE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [901] FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE TRUE FALSE TRUE FALSE
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## [937] FALSE FALSE TRUE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE
## [949] FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
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## [973] FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE
## [985] FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE
## [997] FALSE FALSE TRUE FALSEnum_NAs<-sum(ind)
num_NAs## [1] 1326#q8:Now compute the average again, but only for the entries that are not NA. Hint: remember the !operator.
mean(na_example[!ind])## [1] NaN#q9:Previously we created this data frame:
temp <- c(35, 88, 42, 84, 81, 30)
city <- c("Beijing", "Lagos", "Paris", "Rio de Janeiro", "San Juan", "Toronto")
city_temps <- data.frame(name = city, temperature = temp)
city_temps## name temperature
## 1 Beijing 35
## 2 Lagos 88
## 3 Paris 42
## 4 Rio de Janeiro 84
## 5 San Juan 81
## 6 Toronto 30temp<-5/9*(temp-32)
temp## [1] 1.666667 31.111111 5.555556 28.888889 27.222222 -1.111111#q10:What is the following sum 1 + 1/22 + 1/32 + . . . 1/1002? Hint: thanks to Euler, we know it should be close to π2/6.
x<-c(1:1000)
x## [1] 1 2 3 4 5 6 7 8 9 10 11 12 13 14
## [15] 15 16 17 18 19 20 21 22 23 24 25 26 27 28
## [29] 29 30 31 32 33 34 35 36 37 38 39 40 41 42
## [43] 43 44 45 46 47 48 49 50 51 52 53 54 55 56
## [57] 57 58 59 60 61 62 63 64 65 66 67 68 69 70
## [71] 71 72 73 74 75 76 77 78 79 80 81 82 83 84
## [85] 85 86 87 88 89 90 91 92 93 94 95 96 97 98
## [99] 99 100 101 102 103 104 105 106 107 108 109 110 111 112
## [113] 113 114 115 116 117 118 119 120 121 122 123 124 125 126
## [127] 127 128 129 130 131 132 133 134 135 136 137 138 139 140
## [141] 141 142 143 144 145 146 147 148 149 150 151 152 153 154
## [155] 155 156 157 158 159 160 161 162 163 164 165 166 167 168
## [169] 169 170 171 172 173 174 175 176 177 178 179 180 181 182
## [183] 183 184 185 186 187 188 189 190 191 192 193 194 195 196
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## [211] 211 212 213 214 215 216 217 218 219 220 221 222 223 224
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## [267] 267 268 269 270 271 272 273 274 275 276 277 278 279 280
## [281] 281 282 283 284 285 286 287 288 289 290 291 292 293 294
## [295] 295 296 297 298 299 300 301 302 303 304 305 306 307 308
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## [351] 351 352 353 354 355 356 357 358 359 360 361 362 363 364
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## [379] 379 380 381 382 383 384 385 386 387 388 389 390 391 392
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## [449] 449 450 451 452 453 454 455 456 457 458 459 460 461 462
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## [477] 477 478 479 480 481 482 483 484 485 486 487 488 489 490
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## [519] 519 520 521 522 523 524 525 526 527 528 529 530 531 532
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## [561] 561 562 563 564 565 566 567 568 569 570 571 572 573 574
## [575] 575 576 577 578 579 580 581 582 583 584 585 586 587 588
## [589] 589 590 591 592 593 594 595 596 597 598 599 600 601 602
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## [617] 617 618 619 620 621 622 623 624 625 626 627 628 629 630
## [631] 631 632 633 634 635 636 637 638 639 640 641 642 643 644
## [645] 645 646 647 648 649 650 651 652 653 654 655 656 657 658
## [659] 659 660 661 662 663 664 665 666 667 668 669 670 671 672
## [673] 673 674 675 676 677 678 679 680 681 682 683 684 685 686
## [687] 687 688 689 690 691 692 693 694 695 696 697 698 699 700
## [701] 701 702 703 704 705 706 707 708 709 710 711 712 713 714
## [715] 715 716 717 718 719 720 721 722 723 724 725 726 727 728
## [729] 729 730 731 732 733 734 735 736 737 738 739 740 741 742
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## [757] 757 758 759 760 761 762 763 764 765 766 767 768 769 770
## [771] 771 772 773 774 775 776 777 778 779 780 781 782 783 784
## [785] 785 786 787 788 789 790 791 792 793 794 795 796 797 798
## [799] 799 800 801 802 803 804 805 806 807 808 809 810 811 812
## [813] 813 814 815 816 817 818 819 820 821 822 823 824 825 826
## [827] 827 828 829 830 831 832 833 834 835 836 837 838 839 840
## [841] 841 842 843 844 845 846 847 848 849 850 851 852 853 854
## [855] 855 856 857 858 859 860 861 862 863 864 865 866 867 868
## [869] 869 870 871 872 873 874 875 876 877 878 879 880 881 882
## [883] 883 884 885 886 887 888 889 890 891 892 893 894 895 896
## [897] 897 898 899 900 901 902 903 904 905 906 907 908 909 910
## [911] 911 912 913 914 915 916 917 918 919 920 921 922 923 924
## [925] 925 926 927 928 929 930 931 932 933 934 935 936 937 938
## [939] 939 940 941 942 943 944 945 946 947 948 949 950 951 952
## [953] 953 954 955 956 957 958 959 960 961 962 963 964 965 966
## [967] 967 968 969 970 971 972 973 974 975 976 977 978 979 980
## [981] 981 982 983 984 985 986 987 988 989 990 991 992 993 994
## [995] 995 996 997 998 999 1000sum(1/x^2)## [1] 1.643935#11:ompute the per 100,000 murder rate for each state and store it in the object murder_rate. Then compute the average murder rate for the US using the function mean. What is the average?
murder_rate<-murders$total/murders$population *100000
murder_rate## [1] 2.8244238 2.6751860 3.6295273 3.1893901 3.3741383 1.2924531
## [7] 2.7139722 4.2319369 16.4527532 3.3980688 3.7903226 0.5145920
## [13] 0.7655102 2.8369608 2.1900730 0.6893484 2.2081106 2.6732010
## [19] 7.7425810 0.8280881 5.0748655 1.8021791 4.1786225 0.9992600
## [25] 4.0440846 5.3598917 1.2128379 1.7521372 3.1104763 0.3798036
## [31] 2.7980319 3.2537239 2.6679599 2.9993237 0.5947151 2.6871225
## [37] 2.9589340 0.9396843 3.5977513 1.5200933 4.4753235 0.9825837
## [43] 3.4509357 3.2013603 0.7959810 0.3196211 3.1246001 1.3829942
## [49] 1.4571013 1.7056487 0.8871131mean(murder_rate)## [1] 2.779125Note that the echo = FALSE parameter was added to the
code chunk to prevent printing of the R code that generated the
plot.