WIXLIB

4.3 Basics of Statistics – Weighted AveragesVocabulary and symbols – write out what the following mean: Descriptive StatisticsInferential StatisticsMedian MeanModeWeighted averageConcept questions:1. Is it possible that the mean could be more than the median? Explain how this could occur and givean example set of data.2. Is it possible that the mean could be less than the median? Explain how this could occur and give anexample set of data.3. Podric is trying to find the median in the set of data: 10, 14, 16, 20. He says there is no “middle”number so there is no median. Is he correct? Explain.4. Brienne is trying to find the mode in the set of data: 10, 14, 16, 20. She says there is no “most”number so there is no mode. Is she correct? Explain.5. Bran is trying to find the mode in the set of data: 10, 14, 14, 16, 20, 20. He says there are 2 modesbecause both 14 and 20 occur more than the others. He says it’s like a first place tie. Is he correct?Explain.6. Can a set of data have more than one mean? Can a set of data have more than one median? Can a setof data have more than one mode? Explain.7. Can a set of data have no mean? Can a set of data have no median? Can a set of data have no mode?Explain.8. If the mean of a group of 4 quizzes was 85 and the next quiz taken is a 90, does the mean go up ordown? Explain and find the new mean.9. Will the mean, median, or mode be an actual number in the data set? Explain.10. Carl and Daniel are debating medians. Carl says that he can think of a set of data that has a medianof 80, but when one more data value of 85 is added, the new median is smaller. Daniel says this cannever happen. Who is correct? If you say Carl, create a set of data to show your result. If you sayDaniel, explain why it could never happen.11. Alice and Betty are debating modes. Alice says that she can think of a set of data that has a mode of80, but when one more data value of 85 is added, the new data set has two modes. Betty says this cannever happen. Who is correct? If you say Alice, create a set of data to show your result. If you sayBetty, explain why it could never happen.Math 95 – Homework Unit 4 – Page 10

Exercises:12. Sometimes the mean is known as the “balancing point” for a set of data. This exercise will showwhy it is called that.a. Determine the mean of this set of data: 2, 3, 6, 8, 11.b. For each number, find the “data value minus mean”; this is called the deviation. A numberbelow the mean will have a negative deviation and a number above the mean will have a positivedeviation. What is the deviation of a number that is equal to the mean? Why?c. Add up all the deviations – what is the result?13. If you know the mean of a set of data, can you find the sum of the data values?a. x 28 , n 5c. x 61.2 , n 57b. x 137.5 , n 58d. x 37 , n 2314. If you know the sum of a set of data, can you find the mean of the data values?a. x 40, n 10c. x 627, n 75b. x 491, n 25d. x 26.1, n 3015. Find the mean, median, and mode for each set of data. Calculator only, not a computer.a. 5, 9, 13, 13, 2c. 16, 20, 4, 1, 1b. 11, 22, 95, 40, 38, 88d. 7, 103, 7, 9, 28, 9, 3316. Use your computer to find the mean, median, and mode for:a. 12, 112, 214, 15, 18, 18, 19, 20, 21, 23, 11, 16, 18, 23, 31, 14, 20, 18, 12b. 6, 8, 6, 8, 9, 6, 8, 6, 8, 9, 11, 5, 5, 5, 2, 4, 3, 3, 3, 4, 10c. 237, 411, 298, 300, 302, 405, 299, 500, 7, 400, 377, 222, 233, 244, 255, 1817. Find the mean score on the quiz:6Score on Quiz8Number of Students728845917101418. Find the mean weight of the students:85Weight (in pounds)8Number of Students9079512100201052819. If you have a test average (mean) of 75 after 4 tests, and then get a 90 on the next test, what is yournew mean?20. In standard (00-wheel) roulette, what is the weighted average of:a. a bet on a single number where the payouts are 35:1.b. a bet on 4 numbers where the payouts are 8:1.c. a bet on high (18 numbers) where the payouts are 1:1.21. In European (0-wheel) roulette, what is the weighted average of:a. a bet on a single number where the payouts are 35:1.b. a bet on 4 numbers where the payouts are 8:1.c. a bet on 2 numbers where the payouts are 17:1.d. a bet on high (18 numbers) where the payouts are 1:1.Math 95 – Homework Unit 4 – Page 11

22. In a math class, the students earn grades from different categories. Homework is worth 10%,Quizzes are 20%, Exams are 40%, and the Final Exam is 30%.a. Rachelle earns 80% on homework, 50% on quizzes, 60% on exams, and 70% on the final. Whatis her overall grade?b. Jordan earns 60% on homework, 70% on quizzes, 80% on exams, and 60% on the final. What ishis overall grade.c. Jocelyn earns 80% on homework, 80% on quizzes, 80% on exams, and 80% on the final. What isher overall grade?d. Jackson earns 80% on homework, 80% on quizzes, 80% on exams, and 50% on the final. Whatis his overall grade?e. Penny earns 60% on homework, 60% on quizzes, 60% on exams, and 90% on the final. What isher overall grade?23. Calculate the GPA for the student below.ClassCreditsGrade (letter)Math4CEnglish3CChemistry4BYoga1AGrade (points)Quality PointsGrade (points)Quality PointsGrade (points)Quality PointsTotals24. Calculate the GPA for the student below.ClassCreditsGrade 5. Calculate the GPA for the student below.ClassCreditsGrade (letter)Media Arts2CEnglish4DChemistry5ASpanish4CTotalsMath 95 – Homework Unit 4 – Page 12

26. If your GPA is 3.81 after earning 160 quality points, and then you take one 4-unit class and get a D,what will your new GPA be?27. Yogi’s GPA was 2.13 after earning 100 quality points. He then took 16 units and earned a GPA of3.5 on those units. What will his new cumulative GPA be?28. In a class, exams are worth 60% and a project is worth 40%. What is the lowest exam averagepossible to get 70% overall if a student earns 100% on the project?29. In a class, exams are worth 60% and a project is worth 40%. What is the lowest project averagepossible to get 70% overall if a student earns 100% on exams?30. In a class, exams are worth 60% and a project is worth 40%. If a student earns 40% on exams, canthe student pass the class with a 70% overall? Explain.31. In December 2000, Alex Rodriguez signed a contract guaranteeing him 252 million over 10 years,which was 25.2 million per year. In the same year, the Minnesota Twins paid 26 players an averageof 635,365. If A-Rod was traded to the Twins, they would have 27 players what would be theirnew average salary?32. In 1970, baseball had a minimum salary of 12,000 and an average salary of 29,303. In 1985, theminimum salary was 60,000 and the average salary was 371,571.http://www.stevetheump.com/Payrolls.htma. Consider a team in 1970 that had 26 players all making the minimum salary. If one personmaking the average 1985 salary was added to that group, what would be the new average for theteam?b. Consider a team in 1985 that had 26 players all making the minimum salary. If one personmaking the average 1970 salary was added to that group, what would be the new average for theteam?c. Consider a team in 1985 that had 26 players all making the average salary. If one person makingthe average 1970 salary was added to that group, what would be the new average for the team?d. When you have a large group of people at an average salary, will one person’s salary reallyimpact the average by that much? Explain your conclusion.33. In 2016, on opening day the San Francisco Giants had a total player payroll of 166,495,942. Themean salary for the team was 5,946,284 and the median was 4,000,000. The same year, thePhiladelphia Phillies had a total player payroll of 133,048,000. The mean salary for the team was 4,434,933 and the median was 700,000.a. How many players were on the roster for the Giants?b. How many players were on the roster for the Phillies?c. Based on the information, which team had more low paid players? Why?d. Explain the differences between the mean and median for each team.34. In 2016, the Houston Astros were the team with the lowest player payroll of 69,064,200. Theirmean salary was 2,466,579 and the median salary was 1,031,250.a. Based on these numbers and the previous problem, would you rather play for the Astros or thePhillies? Explain your answer.b. How many people were on the roster for the Astros on opening day?c. The league minimum salary was 507,500. Which team would you wager had more people closeto the league minimum? Why?Math 95 – Homework Unit 4 – Page 13

Wrap-up and look back:35. Interpret the meaning of the mode, meaning, and mean based on used car sales.a. The mean is 11,855.b. The median is 9,502.c. The modes are 7,850 and 12,100.36. If two students are taking the same 3 classes, and each student gets two “B” and one “A” grade, willthey each get the same GPA? Explain.37. Write in words what you learned from this section. Did you have any questions remaining thatweren’t covered in class? Write them out and bring them back to class.4.4: Likelihood AnalysisVocabulary and symbols – write out what the following mean: N/AConcept questions:1. If 67.5% of the data is below 48, what percent is greater than or equal to 48?2. If 40% of the data is a 55 or lower, and 3% of the data is actually a 55, what percent of the data is lowerthan 55?3. If 68.8% of Americans are overweight or obese, and 35.7% of Americans are obese,a. what percent of Americans are overweight?b. what percent of Americans are not obese?c. what percent of Americans are neither overweight nor obese?d. what percent of Americans are not overweight?4. With the coin examples in class, flipping a single coin 100 times led to a mean number of heads. Whatwas the mean number?5. From the coin example, flipping a single coin 100 times led to a mode number of heads. What was themode?6. From the coin example in the book, how many heads (out of 100 flips) would happen less than 20% ofthe time? (there is a high number and a low number)7. From the coin example in the book, how many heads coming up would you say would happen less than30% of the time? (there is a high number and a low number)8. From the coin example in the book, how many heads coming up would you say would happen less than40% of the time? (there is a high number and a low number)9. Intelligence is sometimes measured by using an IQ test. IQ is measured on a scale with a mean andmedian of 100. What does it mean to have a median of 100?Math 95 – Homework Unit 4 – Page 14

Exercises:10. A chart showing IQ and percent of all people is shown below. Compute the cumulative percentages forthe open .1%Math 95 – Homework Unit 4 – Page 15

11. Using the distribution analysis for an IQ test, determine the answers to the following questions. Notethat for this table, all values form 58 to 143 are indicated with bars. The bar directly to the right of a tickmark represents that IQ score.a. At what two IQ scores would 0.5% of the population be located?b. At what two IQ scores would about 2% of the population be located?c. At what two IQ scores would about 1.6% of the population be located?d. What is the most likely IQ score? Would you call this the mean, median, or mode?e. Would you consider this picture to be symmetric?f. About what percent of the population scores a 112?g. About what percent of the population scores a 68?h. About what percent of the population scores a 102?i. Would you say that it is more likely that you find someone who scored a 106 on the IQ test orsomeone who scored an 82? Explain.j. Would you say that it is more likely that you find someone who scored a 142 on the IQ test orsomeone who scored a 75? Explain.k. How likely is it for someone to score a 150 on the IQ test? Explain.Math 95 – Homework Unit 4 – Page 16

12. Using the cumulative distribution analysis for the IQ test, determine the answers to the followingquestions.a. 10% of the population scores at what IQ or lower?b. 20% of the population scores at what IQ or lower?c. 30% of the population scores at what IQ or lower?d. 40% of the population scores at what IQ or lower?e. 50% of the population scores at what IQ or lower?f. 60% of the population scores at what IQ or lower?g. 70% of the population scores at what IQ or lower?h. 80% of the population scores at what IQ or lower?i. 90% of the population scores at what IQ or lower?j. 95% of the population scores at what IQ or lower?k. 5% of the population scores at what IQ or lower?l. Someone scoring a 130 on the IQ test would be rated higher or lower than most of the population?m. In the movie Sneakers (1992), one of the doctors drove around in a vehicle with the custom licenseplace saying “180 IQ.” Based on our data, do you believe the person or think they are beingextremely cocky? Explain.Math 95 – Homework Unit 4 – Page 17

13. Determine the values of the following based on the IQ test. Let X represent the score on the IQ test.Answer these questions.a. P X 100 e. P X 79 b. P X 85 f.c. P X 115 g. P X 105 d. P X 90 h. P X 120 P X 110 14. If X represents the score on a quiz in Math 95, interpret the following:a. P X 100 0.60b. P X 100 0.03c. Use the previous information to find and interpret P X 100 .15. If X represents the weight of a female baby (in pounds) who is 2 years old, interpret the following:a. P X 25 0.40b. P X 33 0.23c. P X 26.5 0.0316. If X represents the weight of a male baby (in pounds) who is 2 years old, interpret the following:a. P X 25 0.28b. P X 33 0.36c. P X 26.5 0.02217. If X represents the height of a male American who is over 18 years old (in inches), interpret thefollowing:a. P X 69 0.50b. P X 84 0.03c. P X 66 0.04Wrap-up and look back:18. Write in words what you learned from this section. Did you have any questions remaining thatweren’t covered in class? Write them out and bring them back to class.4.5: Critical Thinking with Numbers – Simpson’s ParadoxVocabulary and symbols – write out what the following mean: Simpson’s ParadoxConcept questions:1. If 44% of men who applied to a school were admitted and only 35% of women who applied wereadmitted, is your gut instinct that there is a bias against women at the school? Explain.2. If all groups have the same number of participants, and Drug M works better than Drug N, canSimpson’s Paradox apply? Why or why not?Math 95 – Homework Unit 4 – Page 18

3. If a medical study has two groups: Group A receives one drug and Group B receives another. Eachgroup is broken down into 2 smaller subgroups and the percentage of people who are cured by the drugis calculated. Is it possible that both smaller subgroups of Group A are higher than the subgroups ofGroup B, and Group A is higher overall than Group B? Give actual numbers to back up your claim.4. If a medical study has two groups: Group A receives one drug and Group B receives another. Eachgroup is broken down into 2 smaller subgroups and the percentage of people who are cured by the drugis calculated. Is it possible that both smaller subgroups of Group A are higher than the subgroups ofGroup B, but Group B is higher overall than Group A? Give actual numbers to back up your claim.5. If group A is higher in one case and group B is higher in another, is this an indication of Simpson’sParadox? Why or why not?Exercises:6. Consider Drug P and Drug Q, and their successes in different groups of people.Drug P% successDrug QGroup 166 out of 918 out of 10Group 22 out of 923 out of 90% successTotalsa. Determine the %-success for each group and each drug.b. Determine the totals if the groups are combined and the %-success for the drug overall.c. Is this a situation that displays Simpson’s Paradox? Explain why or why not.7. Consider Drug P and Drug Q, and their successes in different groups of people.Drug P% successDrug QGroup 166 out of 918 out of 10Group 28 out of 922 out of 90% successTotalsa. Determine the %-success for each group and each drug.b. Determine the totals if the groups are combined and the %-success for the drug overall.c. Is this a situation that displays Simpson’s Paradox? Explain why or why not.Math 95 – Homework Unit 4 – Page 19

8. Consider Drug P and Drug Q, and their successes in different groups of people.Drug P% successDrug QGroup 166 out of 9161 out of 91Group 28 out of 92 out of 9% successTotalsa. Determine the %-success for each group and each drug.b. Determine the totals if the groups are combined and the %-success for the drug overall.c. Is this a situation that displays Simpson’s Paradox? Explain why or why not.9. Consider Drug P and Drug Q, and their successes in different groups of people.Drug P% successDrug QGroup 175 out of 12583 out of 125Group 298 out of 125112 out of 125% successTotalsa. Determine the %-success for each group and each drug.b. Determine the totals if the groups are combined and the %-success for the drug overall.c. Is this a situation that displays Simpson’s Paradox? Explain why or why not.Wrap-up and look back:10. If Jim saved more money than Stanley on day 1, and Jim saved more money than Stanley on day 2, ifyou combined the savings, who would have more savings? Explain.11. Is the previous question an example of Simpson’s Paradox? Why or why not?12. Why is Simpson’s Paradox considered a “paradox”? What does the word paradox mean?13. In life, is it enough to ‘feel’ that something should be a certain way, or do we need more to show theresults?14. Write in words what you learned from this section. Did you have any questions remaining that weren’tcovered in class? Write them out and bring them back to class.Math 95 – Homework Unit 4 – Page 20

4.6: Wrap-up and ReviewKey concepts in the courses: Gaining an appreciation for number sense Solving linear equations Graphing lines and using slope and intercept to interpret the relationships between input and output Likelihood and probability Expected values and weighted averages Relationships using Venn diagrams Understanding conditional statements and using correct reasoning for arguments Financial awareness and the basics of investing, borrowing, and saving for retirement A clear understanding of the time-value of money Using tables, charts, graphs, and formulas to solve problems Being comfortable with a computer for data entry (and financial predictions) Through repeated problem types, seeing that there is often more than one way to solve a problem Gaining more confidence in computation, interpretation, and understanding the concepts andusefulness of mathematicsWe end with some quotes from Henry Ford that s

Math 95 – Homework Unit 4 – Page 1 Math Fundamentals for Statistics II (Math 95) Homework Unit 4: Connections Scott Fallstrom and Brent Pickett “The ‘How’ and ‘Whys’ Guys” This work is licensed under a Creative Commons Attribution- NonCommercial-Share