The accompanying data set contains three numerical variables, x,, x2. and X3, and one

categorical variable, X4.

a. For X4, how many of the observations are less than three?

continuation of the table: x2 183 78 93 69 89 24 88 130 91 12 165 38 13 153 54 46 21 78 19 200 6 188 121 175 45 17 117 119 153 104 197 120 53 140 91 172 Observation x1 1 0.6709970 2 0.1982038 3 0.8893283 4 0.7494513 5 0.1773418 6 0.0121472 7 0.4720217 8 0.3243587 9 0.6654899 10 0.8410657 11 0.5869552 12 0.6351972 13 0.6611777 14 0.9110208 15 0.7383861 16 0.2994533 17 0.0156395 18 0.7161670 19 0.8618278 20 0.6037751 21 0.5345918 22 0.6555908 23 0.7453034 24 0.4142949 25 0.4030056 26 0.2903282 27 0.2574654 28 0.4099033 29 0.5260399 30 0.0860824 31 0.6031675 32 0.4011186 33 0.3664335 34 0.5772810 35 0.6260032 36 0.8612811 37 0.4176900 38 0.8321404 39 0.1345976 40 0.4090936 41 0.3765112 42 0.3896231 43 0.3687328 44 0.4815050 45 0.9979940 46 0.2509519 47 0.5811088 48 0.1466676 49 0.5140172 50 0.4359606 51 0.8211359 52 0.3891135 53 0.6265650 54 0.8223343 55 0.6579461 56 0.1123249 57 0.5746822 58 0.6699187 59 0.3201346 60 0.7883889 61 0.5890613 62 0.5027353 63 0.7854506 64 0.0367234 65 0.7907019 66 0.7959009 67 0.4412542 68 0.2231531 69 0.8562653 70 0.4252186 71 0.3048715 72 0.7061852 73 0.9138467 x3 1 23 28 3 30 27 3 9 9 9 29 2 16 34 9 11 36 25 27 33 2 2 35 13 37 8 1 5 7 18 37 9 1 10 24 28 31 11 3 3 12 16 25 16 33 2 13 19 33 23 31 30 29 10 38 12 36 2 37 3 13 21 30 18 24 35 12 20 20 37 14 12 38 29 1 x4 1 3 1 2 3 3 2 2 3 1 1 2 1 1 1 1 2 2 2 2 1 2 2 2 3 3 2 1 3 3 2 2 2 2 2 3 2 1 1 2 3 3 1 2 3 1 3 3 1 3 2 3 2 3 1 3 2 2 2 1 2 2 2 3 1 1 2 3 1 2 2 2 2 1 2 2 1 3 1 3 3 2 3 3 74 0.1081561 75 0.5460461 76 0.6419907 77 0.7881503 78 0.2922034 79 0.5867954 80 0.3233733 81 0.9410485 82 0.4264935 83 0.7474799 84 0.2346705 85 0.0246927 86 0.4871749 87 0.9737267 88 0.4305325 89 0.4350979 90 0.6891787 91 0.4962438 92 0.7265224 93 0.2416847 94 0.1792391 95 0.2694641 96 0.7014121 97 0.7023706 98 0.2583090 99 0.2180142 100 0.4251473 101 0.8709118 102 0.7958722 103 0.0190775 104 0.6214736 105 0.8518604 106 0.2445784 107 0.0659970 108 0.1079622 109 0.5581485 110 0.6627794 TI VIRT 111 0.3509706 112 0.7196860 113 0.7403899 114 0.2262354 115 0.2339095 116 0.1731945 117 0.3775797 118 0.1215624 11 17 116 16 146 129 22 159 89 173 140 197 142 136 84 24 72 107 22 169 181 79 5 153 29 71 108 155 79 17 162 151 113 134 189 79 154 35 27 13 10 1 22 25 31 35 1 6 25 28 12 39 22 28 23 8 3 15 30 20 4 8 5 5 37 21 10 15 39 5 14 33 17 34 20 2 14 13 7 15 11 7 13 27 1 3 3 1 3 1 2 2 1 2 2 3 1 2 3 3 1 2 1 2 1 1 2 1 2 2 1 2 2 2 1 1 3 2 2 3 1 3 178 50 10 39 63 33 160 162 3 1 1 2 1 3 1 1 1 49 80 93 125 181 48 198 196 196 51 97 94 70 81 9 61 81 11 39 117 189 160 186 16 179 89 2 156 177 164 191 188 38 31 159 131 143