Chapter 1 Homework Problems
1.1FUEL-EFFICIENT CARS here is a small part of the data set that describes the fuel economy (in miles per gallon) of 1998 model motor vehicles:
Make and Model / Vehicle Type / Transmission Type / Number of Cylinders / City MPG / Highway MPGBMW 3I8I / Subcompact / Automatic / 4 / 22 / 31
BMW 3I8I / Subcompact / Manual / 4 / 23 / 32
Buick Century / Midsize / Automatic / 6 / 20 / 29
Chevy Blazer / 4-Wheel Drive / Automatic / 6 / 16 / 20
a. What are the individuals in this data set?
b.For each individual, what variables are given? Which of these variables are categorical and which are quantitative?
1.2MEDICAL STUDY VARIABLES Data from a medical study contain values of many variables for each of the people who were the subjects of the study. Which of the following variables are categorical and which are quantitative?
a.Gender (Male or Female)
b.Age (Years)
c.Race (Asian, Black, White, Hispanic, or other)
d.Smoker (Yes or No)
e.Systolic Blood Pressure (millimeters of mercury)
f.Level of calcium in the blood (micrograms per milliliter)
1.3Popular magazines often rank cities in terms of how desirable it is to live and work in each city. Describe five variables (categorical or quantitative) that you would measure for each city if you were designing such a study. Give reason for each of your choices.
1.4OLYMPIC GOLD Athletes like Cathy Freedman, Rulon Gardner, Ian Thorpe, Marion Jones, and Jenny Thompson captured public attention by winning gold medals in the 2000 Summer Olympic Games in Sydney, Australia. The table below represents the number of gold medals won by several countries in the 2000 Summer Olympics.
COUNTRY / GOLD METAL WONS / COUNTRY / GOLD METAL WONS / COUNTRY / GOLD METAL WONSSri Lanka / 0 / Switzerland / 9 / Greece / 13
Qatar / 0 / Armenia / 0 / Mozambique / 1
Vietnam / 0 / Kuwait / 0 / Kazakhstan / 3
Great Britain / 28 / Bahamas / 1 / Netherlands / 12
Norway / 10 / Kenya / 2 / India / 0
Romania / 26 / Trinidad/Tobago / 0 / Georgia / 0
Kyrgyzstan / 0 / Costa Rica / 0 / Brazil / 0
Uzbekistan / 1 / Thailand / 1 / Denmark / 2
Latvia / 1 / CzechRepublic / 2 / Hungary / 8
Sweden / 4 / Uruguay / 0 / United States / 39
Make a dot plot of the data. Describe the distribution of the number of gold medals won (Shape, Center, Spread, Outliers).
1.5.Highway gas mileage for model year 2000 midsize cars
Model / MPG / Model / MPGAcura 3.5 RL / 24 / Lexus GS300 / 24
Audi A6 Quattro / 24 / Lexus LS400 / 25
BMW 7401 Sport M / 21 / Lincoln-Mercury LS / 25
Buick Regal / 29 / Lincoln-Mercury Sable / 28
Cadillac Catera / 24 / Mazda 626 / 28
Cadillac Eldorado / 28 / Mercedes-Benz E320 / 30
Chevy Lumina / 30 / Mercedes-Benz E430 / 24
Chrysler Cirrus / 28 / Mitsubishi Diamante / 25
Dodge Stratus / 28 / Mitsubishi Galant / 28
Honda Accord / 29 / Nissan Maxima / 28
Hyundai Sonata / 28 / Oldsmobile Intrigue / 28
Infiniti I30 / 28 / Saab 9-3 / 26
Infiniti Q45 / 23 / Saturn LS / 32
Jaguar VandenPlas / 24 / Toyota Camry / 30
Jaguar S/C / 21 / Voltswagon Passat / 29
Jaguar X200 / 26 / Volvo S70 / 27
Make a dot plot of the data. Describe the distribution of gas mileage (Shape, Center, Spread). Are there any potential outliers?
1.6 The following are the numbers of league-leading runs batted in (RBIs) for baseball’s American league during a recent 50 year period. Display the data in a stem-and-leaf plot. What can you conclude?
115 / 159 / 129 / 105 / 145 / 126 / 116 / 130 / 114 / 122112 / 112 / 142 / 126 / 118 / 118 / 108 / 122 / 121 / 109
140 / 126 / 119 / 113 / 117 / 118 / 109 / 109 / 119 / 139
139 / 122 / 78 / 133 / 126 / 123 / 145 / 121 / 134 / 124
119 / 132 / 133 / 124 / 129 / 112 / 126 / 148 / 147 / 144
1.7SHOPPING SPREE! A marketing consultant observed 50 consecutive shoppers at a supermarket. One variable of interest was how much each shopper spent at the supermarket. One variable of interest was how much each shopper spent in the store. Here is the data in dollars, arranged in increasing order:
3.11 / 8.88 / 9.26 / 10.81 / 12.69 / 13.78 / 15.23 / 15.62 / 17.00 / 17.3918.36 / 18.43 / 19.27 / 19.50 / 19.54 / 20.16 / 20.59 / 22.22 / 23.04 / 24.47
24.58 / 25.13 / 26.24 / 26.26 / 27.65 / 28.06 / 28.08 / 28.38 / 32.03 / 34.98
36.37 / 38.64 / 39.16 / 41.02 / 42.97 / 44.08 / 44.67 / 45.40 / 46.69 / 48.65
50.39 / 52.75 / 54.80 / 59.07 / 61.22 / 70.32 / 82.70 / 85.76 / 86.37 / 93.34
a.Round each amount to the nearest dollar, and then make a stemplot.
b.Make another stemplot by splitting the stems. Which of the plots gives a better distribution?
c.Describe the shape, center, and spread of the distribution. Write a few sentences describing the amount of money spent by shoppers at this supermarket.
1.8Here are the numbers of home runs that Babe Ruth hit in his 15 years with the New York Yankees, 1920-1934:
54 / 59 / 35 / 41 / 46 / 25 / 47 / 60 / 54 / 46 / 49 / 46 / 41 / 34 / 22Babe Ruth’s homerun record for a single year was broken by another Yankee, Roger Maris. Here are the numbers for Maris’s home run total for his 10 years in the American League:
15 / 28 / 16 / 39 / 61 / 33 / 23 / 26 / 8 / 13Make a back-to-back stemplot with Ruth’s data on the left and Maris’s data on the right. Describe the distribution of each player. Who was the better overall hitter?
Make a time-plot of Ruth’s distribution of homeruns from 1920 to 1934.
1.9CEO SALARIESIn 1993, Forbes magazine reported the age and salary of the chief executive officer (CEO) of each of the top 58 small businesses. Here are the salary data, rounded to the nearest thousand dollars:
145 / 621 / 262 / 208 / 362 / 424 / 339 / 736 / 291 / 58498 / 643 / 390 / 332 / 750 / 368 / 659 / 234 / 396 / 300
343 / 536 / 217 / 298 / 1103 / 406 / 254 / 862 / 204 / 206
250 / 21 / 298 / 350 / 800 / 726 / 370 / 536 / 291 / 808
543 / 149 / 350 / 242 / 198 / 213 / 296 / 317 / 482 / 155
802 / 200 / 282 / 573 / 388 / 250 / 396 / 572
Construct the histogram for these data. Describe the shape, center, and spread of the distribution of CEO salaries. Are there any apparent outliers?
1.10BARRY BONDS VERSUS HANK AARON Below is a list of homeruns that Barry Bonds hit for his first 16 years as a major league baseball player:
16 / 25 / 24 / 19 / 33 / 25 / 34 / 46 / 37 / 33 / 42 / 40 / 37 / 34 / 49 / 73a.Find the mean and median of data.
b.Let’s assume 73 is an outlier. Recalculate the median. How was the median affected by the outlier?
Hank Aaron played for the Atlanta Braves for 21 years. The data for the number of homeruns hit by Aaron is listed:
13 / 27 / 26 / 44 / 30 / 39 / 4034 / 45 / 44 / 24 / 32 / 44 / 39
29 / 44 / 38 / 47 / 34 / 40 / 20
c.Find the mean and median number of homeruns for Aaron. Who had the better average when Bond’s outlier of 73 is included? What if the value 73 is excluded?
d.Make a stemplot for Bond’s distribution of homeruns. Describe the distribution.
1.11From the information given in Question 8 find a 5-Number summary for Babe Ruth, and then for Roger Maris. Then create a boxplot for each.
a.Describe the distribution for each. Who was more consistent? How does your boxplot support you answer.
b.Perform a test of outliers for Babe Ruth’s list, and for Roger Maris’s list.
1.12From Question 10, verify that Barry Bond’s homerun count of 73 is an outlier using the outlier test. Are there any outliers in hank Aaron’s set of data? Verify your answer using the outlier test.
1.13The level of various substances in the blood influences our health. Here are measurements of the level of phosphate in the blood of a patient, in milligrams of phosphate per deciliter of blood, made on 6 consecutive visits to a clinic:
5.6 / 5.2 / 4.6 / 4.9 / 5.7 / 6.4a.Find the mean of the 6 observations.
b.Find the variance, and then find the standard deviation.
c.Verify your work using the graphing utility.
1.14From Question 1.8, Roger Maris’s mean number of homeruns is . Find the standard deviation s from its definition.
1.15Listed below is the salary distribution of the 2009-2010 Phoenix Suns basketball team. For the players that have listed salaries, what is the mean salary? What is the standard deviation?
NBA Phoenix Suns Roster 2009 - 2010NO. / PLAYER NAME / POS / AGE / HT / WT / COLLEGE / 2009 - 2010 NBA SALARY
17 / Louis Amundson / PF / 26 / 6-9 / 238 / UNLV / $855,189
10 / Leandro Barbosa / SG / 26 / 6-3 / 202 / $6,600,000
55 / Earl Clark / F / 21 / 6-10 / 225 / Louisville / $1,766,280
02 / GoranDragic / PG / 23 / 6-3 / 190 / $1,836,000
3 / Jared Dudley / SF / 24 / 6-7 / 225 / BostonCollege / $1,307,640
8 / Channing Frye / C / 26 / 6-11 / 245 / Arizona (BOOO!!!!) / $1,990,000
32 / Taylor Griffin / F / 23 / 6-7 / 238 / Oklahoma / $457,588
33 / Grant Hill / SF / 37 / 6-8 / 225 / Duke / $3,000,000
15 / Robin Lopez / C / 21 / 7-0 / 255 / Stanford / $1,745,520
13 / Steve Nash / PG / 35 / 6-3 / 178 / Santa Clara / $13,125,000
23 / Jason Richardson / SG / 28 / 6-6 / 225 / Michigan State / $13,333,332
1 / AmareStoudemire / PF / 26 / 6-10 / 249 / Perry High School / $16,378,325
29 / Alando Tucker / SF / 25 / 6-6 / 205 / Wisconsin / $1,071,720
1.16Let’s assume for the upcoming season, all players received a $2 million raise from the 2009-2010 season. What is the new mean? What is the new standard deviation? How do those calculations compare to mean and standard deviation from Question 1.15?