6. The scatter diagram below shows scores on the midterm and final in a certain
ID: 3041872 • Letter: 6
Question
6. The scatter diagram below shows scores on the midterm and final in a certain course. (a) Was the average midterm score around 25, 50, or 75? (b) Was the SD of the midterm scores around 5, 10, or 20? (c) Was the SD of the final scores around 5, 10, or 20? (d) Which exam was harder-the midterm or the final? (e) Was there more spread in the midterm scores, or the final scores? (1) True or false: there was a strong positive association between midterm scores and final scores. 100 80 60 20 0 20 40 6 80 100 MIDTERM SCOREExplanation / Answer
(a) Average midterm score was around 75. We can see the scatter plot in along the horizontal axis and observe that approximate middle value in the horizontal direction is certainly not 25 or 50. Infact the smallest midterm score is nealy 60. So 75 is the only possible answer.
(b) SD of midterm score is around 10. As observed from the scatter plot, most of the data points are falling inside the interval of length 10 on both sides of the mean 75 along horizontal axis. The answer can not be 5 because the data points are not that densely distributed around mean nor the answer can be 20 because data is not that sparsely distributed along midterm axis.
(c) SD of final score is around 20. As observed from the scatter plot, most of the data points are falling inside the interval of length 20 on both sides of the mean approximately 60 along vertical axis. The answer can not be 5 or 10 because the data points are not that densely distributed around mean along the vertical axis. The fluctuations are large enough along vertical axis to conclude that SD of final score is 20.
(d) Clearly, the final exam is harder than midterm beacuse mean score in final exam is approximately 60, which is less than the mean score in midterm exam which is approximately 75.
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