2.28 The Wall Street Journal is probably referring to the average number of cubes used per glass measured for some population that they have chosen.

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1 .5 x 54.5 a. x b. The raked observatos are: 7.4, 7.5, 7.7, 7.8, 7.9, 8.0, 8.. Sce the sample sze 7 s odd, the meda s the (+)/ 4 th raked observato, or meda 7.8 c. The cosumer would more lkely be terested the compay wth the hghest or maxmum satsfacto ratg..8 The Wall Street Joural s probably referrg to the average umber of cubes used per glass measured for some populato that they have chose..30 x 9 a. x 9. 0 b. To fd the meda, the observatos are raked from smallest to largest: 5, 6, 8, 9, 9, 0, 0, 0,, 3 Sce 0 s eve, the meda s the average of the / 5 th ad ( / ) + 6 th raked observatos, or meda (9+0) / 9.5 c. Sce the mea ad the meda are almost the same, the data s early symmetrc. Therefore, ether the mea or the meda provdes a good measure of the ceter of the dstrbuto..34 x a. x 6 b. The followg table wll be helpful calculatg the stadard devato s: x x x ( x x)

2 Total 0 0 The, s ( x x) s.5.58 or, usg the computatoal formula, we have: s x x s Usg the defto of percetles gve the text, we ca coclude that: $0,000 s the 60 th percetle, $30,000 s the 78 th percetle, ad $40,000 s the 87 th percetle.6 The ordered data are gve the text. () The mmum of the whole data set s 9., ad the maxmum of the whole data set s 3.8. () The meda s the average of the 5 th ad the 6 th observatos (ts posto s ( + ) 5.5 ): meda 5.. Note that there are two alteratve ways to determe the st quartle Q ad the 3 rd quartle Q 3, whch gve approxmately the same aswers. Ay of them wll be cosdered correct. Way (from the lecture otes of Prof. Wag): The posto of Q s 0.5( + ) 0.5(5). 75. That s, we eed to terpolate betwee the th ad the 3 th observatos the followg way: Q (.8.8). 8 The posto of Q 3 s 0.75( + ) 0.75(5) That s, we eed to terpolate betwee the 38 th ad the 39 th observatos the followg way: Q ( ) Way : The frst quartle s the meda of the lower half of the observatos,.e., the average of the 3 th ad the 4 th observatos: Q. 8

3 The thrd quartle s the meda of the upper half of the observatos,.e., the average of the 37 th ad 38 th observatos: Q The boxplot, usg the results from the Way computatos, s gve the fgure below: To check for outlers, we compute (usg the results from the Way computatos): Q.5 IQR.8.5(8.8) 5.47 ad Q +.5 IQR (8.8) Clearly, there are o observatos below There are, however, there are sx observatos above Those are the outlers: 57.4, 6., 65., 00.8, 03.5, ad 3.8. Note that 57.4, 6. ad 65. are very close to the upper fece, so although we classfy them as outlers, they wo t fluece (skew) our sample statstcs (lke sample mea ad sample stadard devato) as much as 00.8, 03.5, ad 3.8 would..64 a. Ethc org s a qualtatve varable sce a qualty (ethc org) s measured. b. Score s a quattatve varable sce a umercal quatty (0-00) s measured. c. Type of establshmet s a qualtatve varable sce a category (Carl s Jr., McDoalds or Burger Kg) s measured. d. Mercury cocetrato s a quattatve varable sce a umercal quatty s measured.

4 .65 a. The umber of ew clets acqured by a law frm a moth s a dscrete varable sce t ca take oly the values 0,, b. The shelf lfe of a partcular drug s a cotuous varable, sce t ca be ay of the fte umber of postve real values. c. The weght of a ralway carload of wheat s a cotuous varable. d. The velocty of a ptched baseball s a cotuous varable e. Ths s a dscrete varable sce t ca take oly the values 0,,.75 The aswer ca vary depedg o the choce of class boudares. As a example, we calculate the rage to be R We could use te classes of legth., or we could use seve classes of legth.3. Usg the latter, we obta the tabulato. class class boudares tally f Relatve Frequecy, f / Here, the lowest pot of dvso s chose just the smallest observed measuremet. The relatve frequecy hstogram s show Fgure It s gve that P (E ) P (E ).5 ad P (E 3 ).4. Sce the probabltes of the dvdual outcomes a expermet sum to ( P (E ) ), we have: () P (E 4 ) + P(E 5 ) () P (E 4 ) *P (E 5 )

5 We have two equatos wth two ukow that ca be solved smultaeously for P (E 4 ) ad P(E 5 ). Substtutg equato () to equato (), we have *P (E 5 ) + P (E 5 ).3 3*P (E 5 ).3, so that P (E 5 ). The, from (), P (E 4 ) +..3 ad P(E 4 ). 3.6 a. There are thrty-eght smple evets, each correspodg to a sgle outcome of the wheel s sp. The thrty-eght smple evets are dcated below. E : Observato a E 37 : Observato a 37 E : Observato a E 38 : Observato a 38 b. Sce ay pocket s just as lkely as ay other, P (E ) /38 c. The evet A cotas two smple evets, E 37 ad E 38. The, P (A) P (E 37 )+P(E 38 ) / 38 / 9. d. Defe evet B as the evet that you w o a sgle sp. Sce you have bet o the umber through 8, evet B cotas eghtee smple evets, E, E,, E 8. The, P(B) P (E ) + P (E ) + + P (E 8 ) 8 / 38 9 / The two-way table gve the exercse shows the four possble smple evets ad ther assocated probabltes. For clarty, defe the four smple evets as follows: E : adult s male ad lves the suburbs E : adult s male ad lves the cty E 3 : adult s female ad lves the suburbs E 4 : adult s female ad lves the cty a. P [customer resdes suburbs] P (E ) + P (E 3 ) b. P [customer s female ad lves the cty] P (E 4 ). c. P [customer s male] P (E ) + P (E ) Defe followg evets G: stock market gas 00 pots or more L: stock market loses 00 pots or more N: stock market chages less tha 0 pots The expermet cossts of pars of forecasts, each of whch wll be oe of the three evets defed above. A tree dagram wll assst fdg these smple evets.

6 G / (a) GG LG NG G-- L \ GL LL NL N GN LN NN G / L-- L \ N G / N L \ N b. The smple evets A are GG, GN, NG, GL, ad LG. c. The smple evets B are GG, LL, ad NN. d. Sce each aalyst s as lkely to select ay oe of the three choces as ay other, P (E ) / 9 ad P (A) 5 / 9. e. P (B) 3 / 9 / 3.