3. (25 Marks) It is well known that there are, at least, three numerical measures of the center for a set of data: Mean, Median, and Mode. (a) (10 Marks) Define the three terms in words clearly. (Hint: The detailed proce- dure for calculating each of them is not necessary!) (b) Explain in detail which one of the above three measures should be used for each of the following cases: i. (6 Marks) An instructor of Course ECON 9999 determines the overall grade from all midterm exams and final exam; ii. (6 Marks) A family is considering to immigrate either to US or Canada based on the information of all the family incomes of the two countries; and iii. (3 Marks) A manager of shoe store wants to know what the most frequently occurring size of shoes the customers would like to buy