Homework Directions: 1. Open book, open notes, open collaboration. Do the problems without using technology excessively. 2. Do your own work. Write up your own solution, even though you may collaborate and discuss the solution with other individuals. That is, do not copy another student's work. 3. Show your steps/work to earn credits. 4. Copy question and write your solution on separate paper. 5. Scan your paper as PDF file and upload file to Canvas. S={52.0, 19.1, 8.2, 30.7, 28.9, 69.0, 78.5, 32.9, 74.6, 8.3, 61.9, 53.4, 58.1, 22.3, 35.7, 59.2, 27.5, 70.8, 29.5, 79.7} 1. Consider the above list of numbers. Calculate the mean and median. Show steps. 2. Consider the above list of numbers. Calculate the range and standard deviation and variance. Show steps. 3. Consider the above list of numbers. Construct the box plot of the data. Show work. 4. Enumerate each sample space and compute the probabilities: (a) If either gender is born with equal likelihood, what is the probability that a family with 3 children has exactly 1 boy and 2 girls? (b) If either gender is born with equal likelihood, what is the probability that a family with 3 children has exactly 2 boys and 1 girl? (c) If 3 fair coins are tossed, what is the probability that one gets 2 heads and 1 tail? (d) If 3 fair coins are tossed, what is the probability that one gets 1 head and 2 tails? Algebra review (of some important concepts) 1. Find the solution set of: |X4 2 |1 2. For some set of real numbers {Xk}: Let SST=k=1 N Xk 2 ,SSm=1 N(k=1 N Xk)2 & SSe=k=1 N (Xk-X)2 ,where Xis the arithmetic average (ie, sample mean for sample data {Xk}). Show that SST=SSm+SSefor N = 4 (simplification). Bonus: Solve the problem for an arbitrary value of N. 3. For some set of real numbers {Xk}: Let some arbitrary values of a & m, show that L1=L2 where

L1=ak=1 N1 N(Xk-m2) & L2=a(S2+(Xm)2)& S2=k=1 N1 N(Xk-X)2 when N = 4 (simplification) & Xis the arithmetic average (ie, sample mean for sample data {Xk}). solve the problem for an arbitrary value of N.