Midterm Version 2 Solutions

Transcription

1 Econ 45 Fall 07 age UIVERSITY OF VICTORIA Mdterm Verson Solutons October 07 AME: STUDET UMBER: V00 Course ame & o. Descrve Statstcs and robably Secton(s) Economcs 45 A0 CR: 098 Instructor: Betty Johnson Duraton: 60 mnutes Ths exam has a total of _5_ ages ncludng ths cover age. Students must count the number of ages and reort any dscreancy mmedately to the Invglator. Ths exam s to be answered: In Booklets rovded Markng Scheme:. 5 marks. 6 marks 3. 0 marks 4. 4 marks Materals allowed: on-rogrammable calculator

2 Econ 45 Fall 07 age Queston : (5 Marks) rove that the oulaton varance can be eual to the followng: ( X ) X where = oulaton sze X X X Snce X ( ) X Exand X X X Take summaton oerator through X X then: = X Queston : (6 Marks) The followng table of data relates to the number of Toones collected n a month by students n several grade 8 classes: (Ths s a oulaton of data.) Interval (# of cons) Freuency 0 < x < x < x < x < x 00 4 Comute the () mode, mode=70, or 60 to 80 (0)(5) (30)(7) (50)(9) (70)(30) (90)(4) 3970 () arhmetc mean,

3 Econ 45 Fall 07 age 3 () the medan 38 th observaton: 50, or 40 to 60 (v) the varance: ( ) (5) ( ) (7) ( ) sheard' s correcton (9) ( ) (30) ( ) (4) (v) the standard devaton (v) coeffcent of varaton. C. V % Queston 3: (0 marks) (a) Use the followng data to construct the aasche rce ndex for 000, wh a base value of 00 n 995: (Table your answer wh the two entres.) (3 Marks) 0 t Good rce Quanty rce Quanty ears tomatoes (4)(38) (6)(5) (3)(38) (5)(5) 89 Year Index (b) Generate the Lasreyres rce ndex wh a base value of 00 n 995. (3 marks) L 0 t 00 (4)(40) (6)(0) (3)(40) (5)(0) 0 (c) Determne whether the Fsher rce ndex asses the tme reversal test usng the data above. (4 Marks) F L Fsher:

4 Econ 45 Fall 07 age 4 t0 00 (3)(40) (5)(0) (4)(40) (6)(0) 80 L t0 00 (3)(38) (5)(5) (4)(38) (6)(5) 4 F L t F F t 0 t 0 test: asses Queston 4: Evews (4 Marks) Assume Heght s a samle of data. () Determne the standard devaton () Determne erson s measure of skewness. (mean-medan)/ standard devaton

5 Econ 45 Fall 07 age 5 mean medan skew s / skew () Determne coeffcent of varaton. ( /55.3) *00=.556 % (v) What s the 76 th ercentle? The 8 th observaton = K 076 locaton Queston 5: (5 marks) Select the most arorate answer n each case and record ths n your answer book. Each art s worth mark. (You may gve a very bref exlanaton f you wsh to, but ths s not necessary.) ) For the followng oulaton of data, {5, 5, 8, 7, 6, 9}, all n Kg., A) *the smle arhmetc mean s 0 Kg. and the geometrc mean s 9.54 Kg. B) the medan s.5 Kg. C) the geometrc mean s 9.54 Kg. and the range s 4 Kg. D) the arhmetc mean s less than the geometrc mean, because the data are "skewed". ) Consder the followng data: Income ($'000) Freuency Cumulatve Freuency 0 < x < x < x < x A) the mean and modal ncomes are both $700,000. B) the modal ncome grou s the $400,000 - $600,000 grou, and the medan ncome grou s the $600,000 - $800,000 grou. C) the mean ncome s $470,000 and the medan ncome s $300,000. D) *the mean ncome s $470,000 and the medan ncome s $500,000. 3) The wdth of each bar n a hstogram corresonds to the A) mdont of the class B) number of observatons n the class C) boundares of the class D) ercentage of observatons n the class ASWER: C

6 Econ 45 Fall 07 age 6 4) Whch of the followng s not a goal of descrve statstcs? A) Summarzng data B) Dslayng asects of the collected data C) Reortng numercal fndngs D) Estmatng characterstcs of the oulaton ASWER: D 5) A lne grah that connects onts that reresent the cumulatve ercentage of observatons below the uer lm of each class nterval n a cumulatve freuency dstrbuton s known as a(n): A) ogve B) freuency hstogram C) freuency olygon D) scatter lot ASWER: A

7 Econ 45 Fall 07 age 7 Formulae Central Locaton: Arhmetc mean x (Groued data x f x f Weghted arhmetc mean W x w / w Geometrc mean G x f Harmonc mean H x x Dserson: oulaton varance (Mean suared devaton) (Groued data x f ) Sheard's correcton c h Samle varance s x x ( n ) Mean absolute devaton MAD = x Coeffcent of varaton CV = ( / ) 00 ercentles: K k /00 Other Measures: Skewness coeffcent skew = ( - medan) / rce Indces: Laseyres' L = [ ] / [ ] M.E. rce Index: ME aasche's = [ ] / [ ] Fsher's "deal" F = [ L ] / M.E. Quanty Index Quanty Indces: Laseyres' Q L = [ ] / [ ] Tme Reversal test:( * ) Q ME aasche Q = [ ] / [ ] Fsher's "deal" Q F = [ Q Q L ] / t0 Factor Reversal Test: 0 Q0 * )