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University of Illinois, Urbana Champaign *

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Feb 20, 2024

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University of Illinois, Urbana-Champaign CS 361 Homework #1 Esther Hwang January 26, 2024 Question 1 a) As median score is 9 and mean is 10. (x1 + x2 + x3 + x4 + x5)/5 = 10. x1 + x2 + x3 + x4 + x5 = 50. 9 + 9 + 9 + x4 + x5 = 50 x4 + x5 = 23 x4 and x5 should be more than 9. (9 + 9 + 9 + 11 + 12)/5 = 10 and the median is 9. The minimum possible top score is 12 b) The lowest student can be 0 so x1 and x2 can be 0. x4 + x5 = 41 0, 0, 9, 9, 32 The maximum of the possible top score is 32. c) Standard deviation of 9, 9, 9, 11, 12 is sqrt(((9-10)**2 +(9-10)**2 + (9-10)**2 + (11-10)**2 + (12- 10)**2)/4) = 1.4142 d) Standard deviation of 0, 0, 9, 9, 32 is sqrt(((0-10)**2 +(0-10)**2 + (9-10)**2 + (9-10)**2 + (32-10)**2)/4) = 13.0958 Page 1

University of Illinois, Urbana-Champaign CS 361 Question 2 a) Fx, (z) = Pr(Xs, z) differentiating this above function allows fx,(z) = d/dz Fx,(z) = d/dz Fx (oz+ u) =e**(-z*2/2)/sqrt(2pi) it allows Xs similar to N(0, 1) b) Median is -1 and it shows how it can be positively or right-skewed because the mean will be at the right side of the median that has -1. Page 2

University of Illinois, Urbana-Champaign CS 361 Figure 1: Q3-b Figure 2: Q3-c Question 3 a) Based on the IQR calculation, there are no outliers in this dataset of cost and number of megawatts. b) Mean : 461.5603125, Standard deviation 170.12066957318333 c) Mean :0.569735439641486, Standard deviation :0.1871243018960576 d) Code below Figure 3: Q3-d(1) Page 3

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University of Illinois, Urbana-Champaign CS 361 Figure 4: Q3-d(2) Question 4 Q4 Page 4

University of Illinois, Urbana-Champaign CS 361 Figure 5: Q4 Figure 6: Q4- 2 Page 5

University of Illinois, Urbana-Champaign CS 361 Figure 7: Q4-2 Question 5 a) The box plot is created represents the distribution of the number of 3-syllable words for three different groups (Group 1, Group 2, and Group 3). There are few more outliers occurred in Group 3. The median of the words are shown lowest for the group 2 and highest for the group 1. The IQR range is the most spread for group 1. b) “Use a box plot to compare the number of sentences appearing in the ads in magazines in these three groups (Group 1, Group 2, and Group 3). There are visible outliers occurred in Group 3. The median of the words are shown lowest for the group 2 and highest for the group 1. The IQR range is the most spread for group . Figure 8: Q5-a Page 6

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University of Illinois, Urbana-Champaign CS 361 Figure 9: Q5-a Figure 10: Q5-b Page 7

University of Illinois, Urbana-Champaign CS 361 Figure 11: Q5-b Page 8

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