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1 Revew Chapter 1: 1. Elements, Varable, and Observatons:. Type o Data: Qualtatve Data and Quanttatve Data (a) Qualtatve data may be nonnumerc or numerc. (b) Quanttatve data are always numerc. (c) Arthmetc operatons are only meanngul wth quanttatve data. Chapter : Fgure., p Summarzng qualtatve data: Frequency dstrbuton, relatve requency dstrbuton, and percent requency dstrbuton. Bar plot and Pe plot.. Summarzng quanttatve data: Frequency dstrbuton, relatve requency dstrbuton, percent requency dstrbuton, cumulatve requency dstrbuton, cumulatve relatve requency dstrbuton, cumulatve percent requency dstrbuton Hstogram, Ogve, and stem-and lea dsplay. Chapters 3 Measures o Locaton, Dsperson, Exploratory Data Analyss, Measure o Relatve Locaton, Weghted and Grouped Mean and Varance Chapter 4: Tabular and Graphcal Methods: Crosstabulaton (qualtatve and quanttatve data) and Scatter Dagram (only quanttatve data). Numercal Method: Covarance and Correlaton Coecent. Chapter 5: 1. Multple Step Experments, Permutatons, and Combnatons.. Event, Addton Law, Mutually Exclusve Events and Independent Event. 3. Bayes Theorem Example 1 (Chapter 1) A magazne surveyed a sample o ts subscrbers. Some o the responses rom the survey are shown below. Subscrber ID Gender Age Income ($1000) 0006 F 45 1

2 4798 M F M (a) How many elements are n the data set? Wrte them down. (b) How many varables are n the data set? Wrte them down. (c) How many observatons are n the data set? Wrte them down. (d) Whch o the above (Sex, Age, Annual Household Income) are qualtatve and whch are quanttatve? (e) Are the data tme seres or cross-sectonal? [soluton:] (a) 4 elements, subscrbers: 0006, 4798, 91, and (b) 3 varables, Gender, Age, and Income. (c) 4 observatons, (F,, 45), (M, 1, 53), (F, 33, 8) and (M, 38, 30). (d) Quanttatve: Age and Income; Qualtatve: Gender. (e) The data are cross-sectonal. Example (Chapter ) The grades o 10 students on ther rst management test are shown below: 94, 61, 96, 66, 9, 68, 75, 85, 84, 78 Suppose the number o nonoverlappng classes s determned to be 4. (a) Please construct the requency dstrbuton table (ncludng requency, percent requency, cumulatve relatve requency, and cumulatve percent requency) or the data. (b) Construct a hstogram and an ogve. [soluton:] (a) Approxmat e wdth 8.75 wdth 9 4. Class Frequency Percent Frequency Cumulatve Relatve Frequency Cumulatve Percent Frequency Total Example 3 (Chapter 3): For the ollowng data,, 1, 0,, 0,, 1,, 0,, 1,,

3 (a) Compute the mean (b) The standard devaton. (c) The coecent o varaton. (d) The (100/3) th percentle. (e) The 8 th percentle () The mode. (g) The nterquartle range. (h) The ve number summary or the data. () The box plot. (j) Determne the outler. [soluton:] 1 x L (a) x (b) s 1 ( x x ) 1 1 ( 1.5) + ( 1 1.5) + + ( 1 1.5) + ( 1.5) 1 L s (c) C. V x 1.5 (d) 1. The data are The ndex s Thus, 1, s the (100/3) th percentle. 8 (e) The ndex s Thus, the 10 th data n (d),, s the th percentle. () The mode s. (g) Snce Q 1 0.5, Q3, IQR Q Q

4 (h) Mnmum Q1 Q Q3 Maxmum Example 4 (Chapter 3): Suppose we have the ollowng data: Rent Frequency Rent Frequency What are the mean rent and the sample varance or the rent? [soluton:] 10 M 1 x g 70, where s the requency o class M s the mdpont o class and n s the sample sze. Then, Rent M Thus, Rent M For the sample varance, s g M and g ( M x ) 70 1 g x Example 5 (Chapter 5): How many commttees consstng o 3 emale and 5 male students can be selected rom a group o 5 emale and 8 male students? [soluton:] ! 3!! 8! 5!3! 560 4

5 Example 6 (Chapter 5): Assume you are takng two courses ths semester (S and C). The probablty that you wll pass course S s 0.835, the probablty that you wll pass both courses s The probablty that you wll pass at least one o the courses s (a) What s the probablty that you wll pass course C? (b) Is the passng o the two courses ndependent event? (c) Are the events o passng the courses mutually exclusve? Explan. [soluton:] (a) Let A be the event o passng course S and B be the event o passng course C. Thus, A) 0.835, A 0.76, A A c A A) A + A c (b) A 0.76 P ( A A) Thus, events A and B are not ndependent. That s, passng o two courses are not ndependent events. (c) Snce P ( A , events A and B are not mutually exclusve. Example 7 (Chapter 5): You are gven the ollowng normaton on Events A, B, C, and D. A).4, A D).6,., A.3, C).1, A C).04, A D).03 (a) Compute D). (b) Compute A. (c) Compute A C). (d) Compute the probablty o the complement o C. (e) Are A and B mutually exclusve? Explan your answer. () Are A and B ndependent? Explan your answer. (g) Are A and C mutually exclusve? Explan your answer. (h) Are A and C ndependent? Explan your answer. 5

6 [soluton:] (a) P ( D) A D) + A D) A) (b) ( A A P (c) ( ) ( A C) 0.04 P A C 0.4. C) 0.1 P. (d) ( C ) 1 C) P c. (e) No, P ( A () No, P ( A A). (g) No, P ( A C) (h) Yes, A C) A) C) 0. Example 8 (Chapter 5): In a random sample o Tung Ha Unversty students 50% ndcated they are busness majors, 40% engneerng majors, and 10% other majors. O the busness majors, 60% were emale; whereas, 30% o engneerng majors were emales. Fnally, 0% o the other majors were emale. Gven that a person s emale, what s the probablty that she s an engneerng major? [soluton:] Let A1: the students are engneerng majors A: the students are busness majors A 1 A A3 Ω A3: the students are other majors. B: the students are emale. Orgnally, we know A1) 0.4, A) 0.5, A3) 0.1, B A1) 0.3, B A) 0.6, B A3) 0.. Then, by Bayes theorem, A1) B A1) A1 A1) B A1) + A) B A) + A3) B A3)