Samp.1 Samp.2 Samp.3 1 88 119 91 2 166 116 98 3 143 92 117 4 110 94 62 5 86 86 51 6 108 81 40 7 133 133 57 8 105 65 74 9 114 82 65 10 126 90 60 11 87 86 26 12 99 98 81 13 72 58 133 14 98 106 174 15 73 99 134 16 137 102 120 17 109 93 119 18 82 101 171 19 122 100 132 20 174 101 88 21 65 126 154 22 99 103 154 23 109 142 94 24 105 103 121 25 79 105 131 __________________________ Median 105 100 98 Mean 108 99 102Based on the sample medians and means (last two rows of the table), the center estimates are fairly similar for the data sets, considering the noise level. So if we would only estimate center it would be hard to tell these data sets apart. But in this class

------------- 1 -------I + I----------------- ------------- ------ 2 * * ---I + I------- * * ------ ----------------------- 3 -------------I + I-------------- ----------------------- ------+---------+---------+---------+---------+---------+C20 30 60 90 120 150 180By the length of the boxes (i.e. interquartile ranges), we see that the noise levels are quite different in the data sets. Sample 3 seems to be twice as noisy as Sample 2 and Sample 2 seems to be twice as noisy as Sample 1. So along with measures of center we need measures of noise. For the third data set the boxplot misses something very important. From the stem leaf plot the data appears to be bimodal. The other two data sets appear to be unimodal.

Stem-and-leaf of Sample 1 N = 25 Leaf Unit = 1.0 1 6 5 4 7 239 8 8 2678 11 9 899 (5) 10 55899 9 11 04 7 12 26 5 13 37 3 14 3 2 15 2 16 6 1 17 4 Stem-and-leaf of Sample 2 N = 25 Leaf Unit = 1.0 1 5 8 2 6 5 2 7 6 8 1266 12 9 023489 (8) 10 01123356 5 11 69 3 12 6 2 13 3 1 14 2 Stem-and-leaf of Sample 3 N = 25 Leaf Unit = 10 1 0 3 3 0 45 8 0 66677 12 0 8999 (1) 1 0 12 1 22223333 4 1 55 2 1 77

Again: you must **PLOT the data** and it is best to **use several different different types of plots**. What do the comparison boxplots tell you (5 extra brownie points)?