The use of placement exams in elementary statistics courses has been a controversial topic in recent times. Some researchers think that the use of a placement exam can help determine whether a student will successfully complete a course (or program). A recent study in a large university resulted in the data listed in Table 1.22. The placement test administered was an in-house written general mathematics test. The course was Elementary Statistics. The students were told that the test would not affect their course grade. After the semester was over, students were classified according to their status. In Table 1.22 are the students’ scores on the placement test (from 0 to 100), and the status of the student (coded as 0 ¼ passed the course, 1 ¼ failed the course, and 2 ¼ dropped out before the semester was over) related?

(a) Construct a frequency histogram for Score. Describe the results.

(b) Construct a relative frequency histogram for Score for each value of Status.
Describe the differences among these distributions. Are there some surprises?

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Table 1.22 Placement scores for elementary statistics. Student Score Status Student Score Status Student Score Status 1 90 10 234567890 65 30 221 36 85 0 71 97 2 37 99 72 90 38 45 0 73 30 0 55 0 39 90 0 74 1 1 40 10 75 5 1 41 56 0 76 70 95 0 42 55 2 77 90 99 0 43 50 0 78 70 40 44 1 1 79 75 95 45 45 11 1 46 50 12 55 0 47 85 13 85 48 95 14 95 0 49 15 00220 80 75 81 70 82 85 83 45 84 50 OOO 22000) 15 15 2 50 35 85 55 16 95 0 51 85 86 15 17 15 0 52 85 87 55 0 18 65 53 50 0 88 20 19 55 54 10 1 89 1 20 75 0 55 60 0 90 75 21 15 0 56 45 1 91 45 22 35 2 57 90 0 92 70 23 90 0 58 1 1 93 70 24 10 0 59 80 2 94 45 25 10 1 60 45 0 95 90 26 20 0 61 90 96 65 27 25 62 45 97 75 28 15 63 20 0 98 70 29 40 30 15 31 50 32 80 33 50 34 50 35 97 oooo120 64 35 1 99 65 65 40 2 100 55 66 40 101 55 67 60 102 40 68 69 70 8800 15 103 56 45 45 55 104 85 0 105 ONOOOO220 ooooooo 80 0