Math 135 S18 Exam 1 Review Name *note: In addition to this Review, study the material from Take Home Assignments, Classwork sheets and class notes. ALL are represented in the exam. The Environmental Protection Agency records data on the fuel economy of many different makes of cars. 1. Some of the variables they collect are listed below. Identify each variable as categorical or numerical. A) The manufacturer of the car B) Mileage of the car. C) Weight of the car D) Size of the car (small, medium, full-size, pick-up truck, etc.). Use the following to answer questions 2-4: In a statistics class with 136 students, the professor records how much money each student has in their possession during the first class of the semester. The histogram shown below represents the data he collected: 2. What is approximately the percentage of students with under $10.00 in their possession? A) 35% C) 44% B) 40% D) 50% 3. Which of the following description(s) is/are correct regarding the shape of the histogram? A) Skewed right D) An outlier is present. B) Skewed left E) Unimodal C) Symmetric F) Bimodal 4. What is approximately the number of students with $30.00 or more in their possession? A) Less than 5 C) About 30 B) About 10 D) More than 100 5. Which center would best describe the data? A) Mean C) Median B) Standard Deviation D) Quartile 1
6. The age of family vehicles owned by residents in a suburban neighborhood can be modeled by a Normal distribution with a mean of 5 years and a standard deviation of 1.5 years. What is the standardized Z value for a family vehicle that is 3 years old? Interpret this Z value. 7. A set of midterm exam scores has a median that is much larger than the mean. Which of the following statements is most consistent with this information? A) A stemplot of the data would be symmetric. B) A stemplot of the data would be skewed left. C) A stemplot of the data would be skewed right. D) The data set must be so large that it would be better to draw a histogram rather than a stemplot. 8-9) During the early part of the 1994 baseball season, many sports fans and baseball players noticed that the number of home runs being hit seemed to be unusually large. Below is a stemplot for the number of home runs by the American League and National League teams. American League National League 2 2 9 3 5 3 1 4 0 3 9 4 2 6 7 8 8 5 1 4 7 8 8 5 3 5 5 5 6 4 8 8 6 3 3 7 7 5 7 7 8. Determine whether each of the following statements is true or false. A) The American League plot is reasonably symmetric. B) The National League plot is bimodal. C) The median number of home runs hit by National League teams for this time period was higher than the median for the American League teams. D) The lowest number of home runs hit by any team for this time period is 29. 9. Using the stemplot above, calculate the mean number of home runs for the National League. A) 50.1 B) 702 C) 5.14 D) 2,192 10. Most of the salaries of Major League Baseball players range within several hundred thousand dollars per year while a few players earn many millions. Which the following statements is most likely to be true: A) A histogram would be skewed to the left B) A histogram would be symmetrical C) The mean would be larger than the median D) The mean would be smaller than the mediana
Use the following to answer questions 11-12: The asking prices (in thousands of dollars) for a sample of 13 houses currently on the market in Neighborville are listed below. Perform all calculations by hand. 299 199 259 549 205 275 175 317 304 345 355 384 234 11. What is the five-number summary? A) 175 234 299 345 549 B) 175 219.5 299 350 549 C) 175 219.5 299 350 384 D) 175 234 299 331 549 12. Use the 1.5 IQR rule to determine if there are any outliers present. What is/are the value(s) of the outlier(s)? A) No outliers present B) One outlier: 175 C) One outlier: 549 D) Two outliers: 175 and 549 13. The fuel efficiency of 2007 model midsized automobiles was studied and the following side-byside boxplots of the distribution of the miles per gallon in city driving (MPG-City) for automobiles manufactured in North America, Asia, and Europe is given below: From these boxplots we can see that: A) The range for European automobiles is approximately B) The maximum miles per gallon is seen in cars. C) The median fuel efficiency rating is lowest for automobiles manufactured in D) The interquartile range for European automobiles is approximately.
14. The five number summary for carbon dioxide emission for 48 countries is as follows: 0.75 3.2 7.8 19.9 a) How many countries had emissions at or below.75? b) Would an emission level of 16 be considered an outlier? Show the calculations that would justify your answer. 15. The asking prices in thousands of dollars for a sample of 20 houses are: 155 160 175 180 199 205 220 234 240 259 275 299 300 304 317 320 345 355 384 390 a) Create an appropriate graph (using StatCrunch) to display the data and describe the shape, center and variability of the distribution. b) Based on the description of the graph, which measure of center should be reported? Explain why. 16. The following nine values represent race finish times in hours for a randomly selected group of participants in an extreme 10k race (a 10k race with obstacles). Which of the following is closest to the mean of the following data set? 1.0, 1.1, 1.2, 1.2, 1.3, 1.4, 1.4, 1.4, 1.5 A 1.1 hours B. 1.3 hours C 1.5 hours D. 1.6 hours 17. The standard deviations for extreme 10k finish times for a randomly selected group of women and men are.17 and.21 respectively. Choose the statement that best summarizes the meaning of the standard deviation. A. On average, men s finish times will be 0.21 hours faster than the overall average finish time. B. On average, women s finish times will be 0.17 hours less than men s finish times. C. The distribution of men s finish times is less varied then the distribution of women s finish times. D. The distribution of women s finish times is less varied then the distribution of men s finish times.
18. The mean age of lead actresses from the top ten grossing movies of 2010 was 29.6 years with a standard deviation of 6.35 years. Assume the distribution of the actresses ages is approximately unimodal and symmetric. Use the Empirical Rule to determine between what two values you expect to find about 95% of the lead actresses ages? A. 23.25 and 35.95 years B. 10.55 and 48.65 years C. 16.9 and 42.3 years D. None of the above 19. The mean price of a pound of ground beef in 75 cities in the Midwest is $2.11 and the standard deviation is $0.56. A histogram of the data shows that the distribution is symmetrical. A local Midwest grocer is selling a pound of ground beef for $3.25. Would this price be unusual or not? A. z = 2.04 ; This is unusually expensive ground beef. B. z = 2.04 ; This price would not be unusual. C. z = 2.04 ; This price would not be unusual. D. z = 2.04 ; This is unusually inexpensive ground beef. 20. The economic impact of an industry, such as sport fishing, can be measured by the retail sales it generates. In 2006, the economic impact of great lakes fishing in states bordering the great lakes had a mean of $318 and a standard deviation of $83.5. Note that all dollar amounts are in millions of dollars. Assume the distribution of retail sales is unimodal and symmetric. (Source: National Oceanic and Atmospheric Administration). Use the Empirical Rule to the percentage of greatlakes states would you expect the economic impact from fishing to be between $234.5 and $401.5 (in millions of dollars)? A. 95% B. 68% C. Nearly all D. None of the above 21. A group of junior high athletes was asked what team sport was their favorite. The data are summarized in the table below. Construct an appropriate graph to summarize the data (use the percents rather than the counts). Then describe what the graph shows. Team Sport # Students Percent Soccer 12 Volleyball 28 Basketball 20 Football 20
KEY 1) A) categorical B) numerical C) numerical D) categorical 2) C 3) A,D,E 4) B 5) C 6) -1.33. 3 year old car is about 1.33 standard deviations below the mean. Not unusual. 7) B 8) T,F,F,T 9) A 10) C 11) B 12) C 13) a) 15 b) Asian c) Europe d) 3 14) a) 12 b) no, only emission levels above 18.375 would be considered outliers. 15) a) histogram, dot plot or stemplot - relatively symetric b) mean 16) B 17) D 18) C 19) A 20) B 21) 15%, 35%, 25%, 25% Bar or pie graph Volleyball most popular, soccer least, somewhat variable.