Mathematics for the Liberal Arts
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Mathematics for Practical Applications - Baseball Exam File Spring 2010 Exam #1 In exercises #1 - 5, a statement is given. For each exercise, identify one AND ONLY ONE of our fallacies that is exhibited in that statement. GIVE A DETAILED EXPLANATION TO JUSTIFY YOUR CHOICE. DO NOT USE THE SAME ANSWER TWICE. 1.) "He's made his last five shots so he's bound to miss this one." 2.) "Who is going to win the World Series this year, the Yankees or the Nationals?" 3.) "Derek Jeter does that Ford commercial so I'm going to buy a Ford. Jeter wouldn't do the commercial if Ford's weren't great cars." 4.) "A-Rod isn't a very good fielding shortstop. After all, in 2008, he had more strikeouts than RBIs." 5.) "Barry Bonds is such a jerk, he can't be the best hitter of all time." 6.) The part of a major league infield that is inside the bases is a square that is 90 feet on each side. How many acres is that? You must show the use of units and conversion factors. 7.) Suppose you went back in time 1,000,000,000 (1 billion) seconds. What year would it be? 8.) If a pitch is thrown 97 miles per hour, how fast is it in meters per second? 9.) CC Sabathia signed a contract with the New York Yankees for $161 million. Convert the contract amount to Mexican pesos. You must show the use of units and conversion factors. 10.) On September 10, 1960, Mickey Mantle hit a home run against Paul Foytack that cleared the right-field roof at Tiger Stadium. Based on where it was found, it was later estimated to have traveled 643 feet. How many millimeters did the ball travel? You must show the use of units and conversion factors. 11.) A person is interested in finding out what college football team people in the United States like most. In order to do that, he does a survey by asking people in Arkansas what their favorite college football team is. Are his results likely to be representative of Americans? Why or why not? 12.) CNN is doing a poll on their web site. Explain why this poll is biased. 13.) For each of the following, tell whether it is an example of a qualitative statistic or a quantitative statistic. a.) height of people who play baseball professionally b.) number of times a batter strikes out with men on base and less than two out c.) eye color of students at Henderson State University d.) percentage of freshmen students at Henderson State University who finish with a GPA of 3.0 or higher 14.) Name five different rule changes or changes in style of play that we discussed that make it difficult to compare statistics over different eras of baseball history. Exam #2 1.) In 1972, Nate Colbert, first baseman of the Padres, had 111 runs batted in. The entire team only scored 488 runs. What percentage of the Padres' runs did Colbert knock in? 2.) In 2004, Albert Pujols of the St. Louis Cardinals was paid $7,000,000. For 2005, his salary went up 57.14285714%. For 2006, his salary went up 27.27272727%. What was his 2006 salary? 3.) A car was on sale for $10,875. That was 13% off the original price. What was the original price? 4.) The following chart shows the number of times Baby Doll Jacobson was hit by pitches (HBP) during 1920 to 1925. Year 1920 1921 1922 1923 1924 1925 HBP 2 3 9 2 4 1 YOU MAY NOT USE YOUR CALCULATOR FOR THIS PROBLEM. YOU MUST SHOW ALL WORK AND GIVE AN EXPLANATION OF HOW YOU GOT YOUR ANSWERS. Find the following for the numbers of HBP in those seasons. a.) the mean b.) the median c.) the mode 5.) The following are the major league leaders in at bats (AB) from 1960. Name AB Name AB Hank Aaron 590 Don Hoak 553 Luis Aparicio 600 Tony Kubek 568 Ernie Banks 597 Jerry Lumpe 574 Ken Boyer 552 Frank Malzone 595 Bill Bruton 629 Willie Mays 595 Orlando Cepeda 569 Minnie Minoso 591 Roberto Clemente 570 Vada Pinson 652 Rocky Colavito 555 Vic Power 580 Nellie Fox 605 Brooks Robinson 595 Billy Gardner 592 Bob Skinner 571 Jim Gilliam 557 Tony Taylor 581 Dick Groat 573 Bill Tuttle 559 Bill White 554 For the above data, find the following. a.) minimum b.) lower quartile c.) median d.) upper quartile e.) maximum f.) mean g.) mode 6.) Comparisons a.) Harmon Killebrew and Tony Oliva both played for the 1966 Minnesota Twins. Killebrew's batting average was .281. Oliva's was .307. Explain why this does not necessarily indicate that Oliva was a better hitter that year. Give at least two reasons. b.) In 1967, Sam McDowell of the Cleveland Indians struck out 236 batters. In 1929, Lefty Grove of the Philadelphia Athletics struck out 170 batters. Explain why this does not necessarily indicate that McDowell was a better strikeout pitcher in 1967 than Grove was in 1929. Give at least two reasons. c.) In 1879, the Providence Grays won 59 games. In 1966, the Chicago Cubs won 59 games. Explain why this does not necessarily indicate that the 1966 Cubs and the 1879 Grays had the same level of success. Give at least two reasons. 7.) The following chart shows some batting statistics for Rogers Hornsby from 1924. Fill in the blanks. At Hits Doubles Triples Home Batting On Base Slugging OPS Total Bats Runs Average Percentage Percentage Bases 536 227 43 14 25 .507 8.) The following are the pitching statistics for Steve Blass in 1973. Fill in the blanks. Wins Losses Winning Earned Run Innings Hits Earned Hits per Percentage Average Pitched Runs inning 3 9 88.66 109 97 9.) The following are the standings for the National League East after the games of September 3, 1986. Team W L PCT GB Magic Number for Mets to eliminate team New York Mets 89 44 --------- --------- Philadelphia Phillies 69 64 .519 St. Louis Cardinals 67 66 .504 Montreal Expos 64 66 --------- --------- Chicago Cubs 55 78 .414 --------- Pittsburgh Pirates 54 78 --------- 10.) The following table gives the major league leaders in OPS from 1930. Fill in the blanks. OPS On Base Average Slugging Percentage 1 Babe Ruth .493 .732 2 Lou Gehrig 1.194 .721 3 Hack Wilson 1.177 .454 4 Babe Herman .455 .678 5 Al Simmons 1.130 .708 6 Chuck Klein 1.123 .436 7 Bill Terry 1.071 .452 .619 8 Jimmie Foxx .429 .637 9 Chick Hafey 1.059 .652 10 Lefty O'Doul 1.057 .453 11.) The following are Lance Alworth's statistics for the 1965 San Diego Chargers. Fill in the blanks. Receiving Rushing Games Receptions Yards Yards per Receptions Attempts Yards Yards Reception per Game per Attempt 14 69 1602 3 -12 12.) The following are Wilt Chamberlain's statistics for the 1961-1962 NBA season. Fill in the blanks. Games Field Field Goals Field Rebounds Rebounds Points Points Goals Attempted Goal per game per % Game 80 1597 3159 2052 4029 13.) The following are some statistics for Lady Reddies volleyball player Quen Banks from 2008. Fill in the blanks. Sets Kills Kills Attack Total Kill played per set Errors attacks Percentage 104 334 141 834 14.) Matching - For each item in Column B, place in the blank the number of the associated name from Column A. Note that there are more choices in Column A than in Column B. No answer should be used more than once. Column A Column B 1.) 1869 Cincinnati Red ________ "The Father of Baseball" Stockings ________ began collecting players' lifetime statistics that were not available 2.) 1884 Troy Trojans anywhere, eventually publishing a book, Who's Who in Baseball, in 1912 3.) Alan Roth ________ hired the first full-time statistician 4.) Albert Spalding ________ In 1977, he published his first Abstract, giving statistics along with analysis and 5.) Art Richmond commentary. According to Schwarz, he did more than anyone else to 6.) Babe Ruth popularize the study of baseball statistics and analysis. 7.) Bill James ________ National League secretary and statistics fanatic, particularly pitching 8.) Bill Veeck statistics ________ star pitcher, manager, helped form 9.) Branch Rickey National League in 1876, started sporting goods company 10.) Henry Chadwick ________ the appeal of his home runs led baseball to try to help increase power 11.) John Heydler hitting 12.) John Lawres ________ the first openly professional team ________ was hired as first full-time statistician 13.) Lee Allen ________ Was the preeminent baseball historian of the era of the 20th century 14.) Richie Ashburn Exam #3 1.) The following chart gives the number of triples Honus Wagner hit during his first eight years in the major leagues. Draw a line graph to illustrate the data. Year Triples 1897 4 1898 3 1899 13 1900 22 1901 11 1902 16 1903 19 1904 14 2.) The following pie chart shows the home run production for the 1962 Giants. a.) Who hit the most home runs for the 1962 Giants? b.) How many players hit home runs for the 1962 Giants? c.) The angle for the portion representing Willie Mays (the greatest all around player in baseball history) is 86.47058824. If the team hit 204 home runs, how many did Mays hit? d.) Three players hit more than 20 home runs. Who were they? 3.) The following chart gives career statistics for Grover Cleveland Alexander.