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Discrete Math Chapter 14 Test Review Name _________________________________ Period ______________ For questions 1 – 8, refer to the table below that shows the scores on an Economics 101 test consisting of 10 questions worth 10 points each. Student ID Score Student ID Score Student ID Score Student ID Score 1362 1486 1721 1932 2489 2766 100 90 80 80 80 60 2877 2964 3217 3588 3780 3921 80 70 70 90 90 90 4315 4719 4951 5321 5872 6533 10 10 60 70 40 60 6921 8317 8854 8964 9158 9347 60 70 80 80 90 70 1. Complete the frequency table for the Econ 101 test. Frequency Table for Economics 101 Test Score Frequency 2. Identify the score that corresponds to each data point. X1 = __________ X3 = __________ X4 = __________ X13 = __________ X23 = __________ 3. What is the size of the data set? N = _______________ 4. Find the sum of the data. X N i 1 i = _______________ 5. Find the mean score, the median score, and the mode for the Econ 101 test. µ = ___________ M = ___________ mode = ___________ 6. Find the five-number summary for the Econ 101 test. Min = ________ Q1 = ________ M = ________ Q3 = ________ Max = ________ 7. Determine outlier scores for the Econ 101 test. If there are no outliers, write “None.” ____________________ 8. Suppose the grading scale for the test is A: 90-100, B: 80-89, C: 70-79, D: 60-69 and F: 0-59. a. Find the grade distribution for the exam. Frequency Table for Grade Distribution Grade Frequency b. Complete the table by (1) determining the percent of students (rounded to one decimal place) that earned each grade on the Econ 101 test and (2) calculating the size of the central angle (rounded to the nearest whole degree) of each grade’s wedge in a pie chart. Then make a pie chart showing the grade distribution for the exam. Grade Percent of Students Central Angle A B C D F c. Make a bar graph showing the relative frequencies of the grades on the test. Be sure to label the axes. 28 24 20 Frequency 16 12 8 4 0 47 49 51 53 55 57 59 61 63 Speed (mph) 9. To determine an appropriate speed limit for a roadway, traffic engineers conduct radar checks of the speeds of passing cars at a selected location and under ideal driving conditions. They then conduct a statistical analysis of the data to determine the safest speed limit to post on the roadway. The histogram above summarizes the data collected on the speed of cars on a roadway. Endpoint convention: Speeds on the boundary of an interval belong in the interval to the right. For example, a speed of 49 mph belongs in the second interval (49-51). a. How many cars were included in this survey? ____________________ b. What is the size of each interval? ____________________ c. How many cars were clocked at 55 mph or more? ____________________ d. Which interval contains the median speed? ____________________ Traffic studies suggest that posting a speed limit at the 85th percentile speed increases compliance among drivers and minimizes traffic accidents and traffic jams. e. What interval contains the 85th percentile speed? ____________________ f. What speed limit would you recommend for this roadway? ____________________ g. Estimate the average (mean) speed of cars surveyed in this study? 10. The table below shows the closing stock prices (in $) on the New York Stock Exchange (NYSE) for the last seven months for General Motors (GM) and Ford. Month Ford GM OCT 11.16 25.50 Closing Stock Price ($) on the NYSE NOV DEC JAN FEB 11.45 12.95 12.95 12.61 25.88 28.83 28.09 27.15 MAR 13.15 27.82 APR 13.12 28.37 a. Find the mean stock price x and the standard deviation s for each auto company (Round all figures to two decimal places). Ford Stock Deviation Deviation Squared xi xi x ( xi x ) 2 x = ____________ n s2 (x i 1 x)2 i n 1 n n (x i 1 i x) s n (x i 1 (x i 1 GM Stock Deviation Deviation Squared xi xi x ( xi x ) 2 x)2 i n 1 x)2 i s2 (x i 1 x)2 i n 1 n s (x i 1 i x) n (x i 1 i x)2 = ____________ x = ____________ n n = ____________ (x i 1 i = ____________ x)2 n 1 = ____________ b. Which stock (Ford of GM) appears to have the greater risk. Explain your answer. c. Determine the outlier prices for Ford stock. If there are no outliers, write “None.” __________________________ d. Determine the outlier prices for GM stock. If there are no outliers, write “None.” __________________________