Test 2 Practice Test #1_____ 1. To estimate the mean age of all students attending her university, a statistician selected a simple randomsample of 15 students. Prior to going on vacation, the statistician collected data for only 13 of the 15students, and determined that the median age of the 13 students was 21 years. The statistician took the datawith her on vacation, so this median value of 21 is all you know about the ages of those 13 students. Youdo, however, now know that the last two students were 19 and 31 years of age, respectively. Based on thisinformation, which of the following best describes the median age of all 15 students in the sample?(A) 25 (B) 21 (C) 21.53 (D) 23.67 (E) Cannot be determined from the information providedA very popular leisure activity in the fall for many people is fantasy football. In fantasy football you draft a team of realNFL players, and compete head-to-head with other fantasy owners with scores based on the real performance of theplayers on your fantasy team. The data below gives the number of rushing and receiving touchdowns scored in week 1of fantasy football for a random sample of 10 teams. Use this data to answer questions 2 through 6. Please write yourfinal answer on the line before the question number. You can use the calculator, or you can choose to do theproblems by hand, in which case any work you show will be considered for partial credit.7 11 8 12 4 6 2 15 7 8__________ 2. Calculate the mean of the data.__________ 3. Calculate the median of the data.__________ 4. Calculate the range of the data.__________ 5. Calculate the standard deviation of the data.__________ 6. Calculate the interquartile range of the data.7. Most fantasy leagues use a standard scoring system where players accumulate points for touchdowns, yardagegained either rushing or passing, kicking, and defensive and special teams plays. The data below give the numberof fantasy points scored by a random sample of 24 fantasy teams that use the standard scoring system. Constructan appropriate stem-and-leaf plot to graphically display this data.91 108 132 68 77 47 79 82 96 54 64 82 106 88 91 60 79 86 97 61 79 119 102 1398. Consider the stem-and-leaf plot constructed in question 7. Use the stem-and-leaf plot to completely describe thedistribution of the standard fantasy scores for this sample of 24 fantasy football teams.9. A few fantasy football leagues use “exotic” rules that often produce many more points than the points scored in astandard scoring league. In one “exotic” scoring league a team scored 432 points, and suppose this score wereadded to the sample of 24 fantasy points presented in question 7. Clearly this value of 432 would be considered anoutlier. For each of the following, circle YES or NO to indicate whether the statement is a correct statement.YES NO The mean is a measure of spread that is heavily influenced by the outlier.YES NO The median is a measure of center that is heavily influenced by the outlier.YES NO The interquartile range is a measure of spread that is resistant to the outlier.YES NO The standard deviation is a measure of center that is resistant to the outlier.Many fantasy football leagues are played for fun only, while others have an entry fee that is then turned into prizes forthe winners. The boxplot below reveals the entry fees for a random sample of 100 fantasy football leagues. Use thisboxplot to answer questions 10 through 12. x-- ------------------------------x • •----------------------------------------------------------------------------------------------------------------------------------------0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170Entry Fee______ 10. Which of the following best describes the spread of this distribution?(A) The median of the data is 10.(B) The range of the data is 80 – 0 = 0.(C) The range of the data is 40 – 5 = 35.(D) The interquartile range of the data is 150 – 0 = 150.(E) The interquartile range of the data is 40 – 5 = 35.______ 11. Which of the following best describes the shape of this distribution?(A) The distribution has outliers at 100 and 150.(B) The distribution is symmetrical.(C) The distribution is skewed to the left.(D) The distribution is skewed to the right.(E) The distribution is trimodal.______ 12. Which of the following best describes the center of this distribution?(A) The range of the data is 150 – 0 = 0.(B) The mean of the data is 10.(C) The median of the data is 10.(D) The median of the data is 22.5.(E) The distribution has outliers at 100 and 150.Questions 13 and 14 are multiple choice questions and question 15 is a true/false question. For questions 13 and14 please write the letter of your answer on the line in front of the question number, and for question 15 pleasewrite True or False on the line in front of the question number.______ 13. Which of the following is a graphical procedure for displaying qualitative data?(A) Stem-and-leaf plot (B) Histogram (C) Box plot (D) All of (A), (B) and (C) (E) None of (A), (B) and (C)______ 14. Which of the following is not a component of a 5-number summary?(A) Median (B) Standard deviation (C) Upper quartile (D) Lower quartile (E) None of the above______ 15. For a given set of data a frequency histogram is constructed. Using the same data and the same classintervals, a relative frequency histogram is constructed. TRUE or FALSE: the frequency histogram and therelative frequency histogram will look the same, except for the labeling of the vertical axis.Test 2 Practice Test #1 Solutions1. B – With n = 13, the median location = (n + 1)/2 = (13 + 1)/2 = 7, so the 7th ordered observation isthe median, 21.With the two values added, n = 15, so the median location = (15 + 1)/2 = 8 Since 19 is less than the median, 21 is now the 8th ordered observation and hence the medianremains unchanged at 21.2. ´X =∑xn=7+11+ …+810=8010=8 3. Median Location = n+12=10+12=112=5 . 5; Median = average of the 5th and 6th orderedobservations = 7 +82=7.5 4. Range = Max – Min = 15 – 2 = 13 5. S = 3.83; see page 77 for how to compute S 6. Median of the 5 smallest observations = Q1 = 6Median of the 5 largest observations = Q3 = 11IQR =
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