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Chapter 02 - Descriptive Statistics: Tabular and Graphical MethodLink download full: SolutionManual for Essentials of Business Statistics 5th Edition by Bowerman https://digitalcontentmarket.org/download/solution-manual-for-essentials-of-businessstatistics-5th-edition-by-bowermanCHAPTER 2—Descriptive Statistics: Tabular and Graphical Methods §2.1 CONCEPTS 2.1Constructing either a frequency or a relative frequency distribution helps identify and quantify patterns that are not apparent in the raw data. LO02-012.2Relative frequency of any category is calculated by dividing its frequency by the total number of observations. Percent frequency is calculated by multiplying relative frequency by 100. LO02-012.3Answers and examples will vary. LO02-01§2.1 METHODS AND APPLICATIONS 2.4a.Test Response A B C DFrequency 100 25 75 50Relative Frequency 0.4 0.1 0.3 0.2Percent Frequency 40% 10% 30% 20%b.2-1 Copyright © 2015 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.Chapter 02 - Descriptive Statistics: Tabular and Graphical MethodBar Chart of Grade Frequency 120 100 100 7580 6050402520 0 ABCDLO02-012-2 Copyright © 2015 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.Chapter 02 - Descriptive Statistics: Tabular and Graphical Method2.5a.(100/250) • 360 degrees = 144 degrees for response (a)b.(25/250) • 360 degrees = 36 degrees for response (b)c.Pie Chart of Question Response Frequency D, 50 A, 100C, 75 B, 25LO02-01 2.6a.Relative frequency for product x is 1 – (0.15 + 0.36 + 0.28) = 0.21b.Product: W X Y Z frequency = relative frequency • N = 0.15 • 500 = 75 105 180 140c.Percent Frequency Bar Chart for Product Preference 36%40%28%30% 20%21% 15%10% 0% Wd.XYZDegrees for W would be 0.15 • 360 = 54 for X 75.6 for Y 129.6 for Z 100.8.LO02-012-3 Copyright © 2015 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.Chapter 02 - Descriptive Statistics: Tabular and Graphical Method2.7a.Rating Outstanding Very Good Good Average PoorFrequency 14 10 5 1 0 ∑ = 30Relative Frequency 14 /30 = 0.467 10 /30 = 0.333 5 /30 = 0.167 1 /30 = 0.033 0 /30 = 0.000b.Percent Frequency For Restaurant Rating 50%47%40%33%30% 17%20% 10%3%0%0% OutstandingVery GoodGoodAveragePoorc.Pie Chart For Restaurant Rating Average, 3%Poor, 0%Good, 17%Very Good, 33%Outstanding, 47%LO02-012-4 Copyright © 2015 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.Chapter 02 - Descriptive Statistics: Tabular and Graphical Method2.8a.Frequency Distribution for Sports League Preference Sports League MLB MLS NBA NFL NHLFrequency 11 3 8 23 5 50Percent Frequency 0.22 0.06 0.16 0.46 0.10Percent 22% 6% 16% 46% 10%b.Frequency Histogram of Sports League Preference 252320 15 11 108 5530 MLBMLSNBANFLNHLc.Frequency Pie Chart of Sports League Preference NHL N = 50, 0 NHL 5, 0.1 MLB 11, 0.22 MLS 3, 0.06 NFL 23, 0.46d.NBA 8, 0.16The most popular league is NFL and the least popular is MLS.LO02-0112-5 Copyright © 2015 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.Chapter 02 - Descriptive Statistics: Tabular and Graphical Method2.9US Market Share in 2005 28.3%30.0%26.3%25.0% 18.3%20.0% 15.0%13.6%13.5%10.0% 5.0% 0.0% Chrysler Dodge JeepFordGMJapaneseOtherUS Market Share in 2005 Chrysler Dodge Jeep, 13.6% Other, 13.5%Ford, 18.3%Japanese, 28.3%GM, 26.3%LO02-01 2.10 Comparing the pie chart above and the chart for 2010 in the text book shows that between 2005 and 2010, the three U.S. manufacturers, Chrysler, Ford and GM have all lost market share, while Japanese and other imported models have increased market share. LO02-012-6 Copyright Š 2015 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.Chapter 02 - Descriptive Statistics: Tabular and Graphical Method2.11 Comparing Types of Health Insurance Coverage Based on Income Level 100% 87%90% 80% 70% 60%50%Income < $30,00050% 40%Income > $75,00033%30% 17%20%9%10%4%0% PrivateMcaid/McareNo InsuranceLO02-012-7 Copyright Š 2015 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.Chapter 02 - Descriptive Statistics: Tabular and Graphical Method2.12 a.Percent of calls that are require investigation or help = 28.12% + 4.17% = 32.29%b.Percent of calls that represent a new problem = 4.17%c.Only 4% of the calls represent a new problem to all of technical support, but one-third of the problems require the technician to determine which of several previously known problems this is and which solutions to apply. It appears that increasing training or improving the documentation of known problems and solutions will help.LO02-02§2.2 CONCEPTS 2.13 a.We construct a frequency distribution and a histogram for a data set so we can gain some insight into the shape, center, and spread of the data along with whether or not outliers exist.b.A frequency histogram represents the frequencies for the classes using bars while in a frequency polygon the frequencies are represented by plotted points connected by line segments.c.A frequency ogive represents a cumulative distribution while the frequency polygon does not represent a cumulative distribution. Also, in a frequency ogive, the points are plotted at the upper class boundaries; in a frequency polygon, the points are plotted at the class midpoints.LO02-03 2.14 a.To find the frequency for a class, you simply count how many of the observations have values that are greater than or equal to the lower boundary and less than the upper boundary.b.Once you determine the frequency for a class, the relative frequency is obtained by dividing the class frequency by the total number of observations (data points).c.The percent frequency for a class is calculated by multiplying the relative frequency by 100.LO02-032-8 Copyright Š 2015 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.Chapter 02 - Descriptive Statistics: Tabular and Graphical Method2.15 a.Symmetrical and mound shaped: One hump in the middle; left side is a mirror image of the right side.b.Double peaked: Two humps, the left of which may or may not look like the right one, nor is each hump required to be symmetricalc.Skewed to the Right: Long tail to the rightd. Skewed to the left: Long tail to the leftLO02-032-9 Copyright Š 2015 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.Chapter 02 - Descriptive Statistics: Tabular and Graphical Method§2.2 METHODS AND APPLICATIONS 2.16 a.Since there are 28 points we use 5 classes (from Table 2.5).b.Class Length (CL) = (largest measurement – smallest measurement) / #classes = (46 – 17) / 5 = 6 (If necessary, round up to the same level of precision as the data itself.)c.The first class’s lower boundary is the smallest measurement, 17. The first class’s upper boundary is the lower boundary plus the Class Length, 17 + 3 = 23 The second class’s lower boundary is the first class’s upper boundary, 23 Continue adding the Class Length (width) to lower boundaries to obtain the 5 classes: 17 ≤ x < 23 | 23 ≤ x < 29 | 29 ≤ x < 35 | 35 ≤ x < 41 | 41 ≤ x ≤ 47d.Frequency Distribution for Values lower 17 23 29 35 41< < < < <upper 23 29 35 41 47midpoint 20 26 32 38 44width 6 6 6 6 6frequency 4 2 4 14 4 28cumulative frequency 4 6 10 24 28percent 14.3 7.1 14.3 50.0 14.3 100.0cumulative percent 14.3 21.4 35.7 85.7 100.0e. Histogram of Value 1414 12Frequency10 8 6 444 22 04172329354147Valuef.See output in answer to d.LO02-032-10 Copyright © 2015 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.Chapter 02 - Descriptive Statistics: Tabular and Graphical Method2.17 a. and b. Frequency Distribution for Exam Scores lower 50 60 70 80 90< < < < <upper 60 70 80 90 100midpoint 55 65 75 85 95width 10 10 10 10 10frequency 2 5 14 17 12percent 4.0 10.0 28.0 34.0 24.050100.0relative frequency 0.04 0.10 0.28 0.34 0.24cumulative frequency 2 7 21 38 50cumulative percent 4.0 14.0 42.0 76.0 100.0c. Frequency Polygon 40.0 35.0Percent30.0 25.0 20.0 15.0 10.0 5.0 0.0 4050607080908090Datad. OgiveCumulative Percent100.075.050.025.00.0 40506070 DataLO02-032-11 Copyright Š 2015 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.Chapter 02 - Descriptive Statistics: Tabular and Graphical Method2.18 a.Because there are 60 data points of design ratings, we use six classes (from Table 2.5).b.Class Length (CL) = (Max – Min)/#Classes = (35 – 20) / 6 = 2.5 and we round up to 3, the level of precision of the data.c.The first class’s lower boundary is the smallest measurement, 20. The first class’s upper boundary is the lower boundary plus the Class Length, 20 + 3 = 23 The second class’s lower boundary is the first class’s upper boundary, 23 Continue adding the Class Length (width) to lower boundaries to obtain the 6 classes: | 20 < 23 | 23 < 26 | 26 < 29 | 29 < 32 | 32 < 35 | 35 < 38 |d.Frequency Distribution for Bottle Design Ratings lower 20 23 26 29 32 35< < < < < <upper 23 26 29 32 35 38midpoint 21.5 24.5 27.5 30.5 33.5 36.5width 3 3 3 3 3 3frequency 2 3 9 19 26 1 60percent 3.3 5 15 31.7 43.3 1.7 100cumulative frequency 2 5 14 33 59 60cumulative percent 3.3 8.3 23.3 55 98.3 100e. Distribution shape is skewed left. Histogram of Rating 26 2519Frequency2015910532 0201 232629 Rating323538LO02-032-12 Copyright © 2015 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.Chapter 02 - Descriptive Statistics: Tabular and Graphical MethodFrequency Distribution for Ratings2.19 a & b. lower 20 23 26 29 32 35< < < < < <upper 23 26 29 32 35 38midpoint 21.5 24.5 27.5 30.5 33.5 36.5relative frequency 0.033 0.050 0.150 0.317 0.433 0.017 1.000width 3 3 3 3 3 3percent 3.3 5.0 15.0 31.7 43.3 1.7 100cumulative relative frequency 0.033 0.083 0.233 0.550 0.983 1.000cumulative percent 3.3 8.3 23.3 55.0 98.3 100.0c. OgiveCumulative Percent100.075.050.025.00.0 17202326293235RatingLO02-03 2.20 a.Because we have the annual pay of 25 celebrities, we use five classes (from Table 2.5). Class Length (CL) = (290 – 28) / 5 = 52.4 and we round up to 53 since the data are in whole numbers. The first class’s lower boundary is the smallest measurement, 28. The first class’s upper boundary is the lower boundary plus the Class Length, 28 + 53 = 81 The second class’s lower boundary is the first class’s upper boundary, 81 Continue adding the Class Length (width) to lower boundaries to obtain the 5 classes: | 28 < 81 | 81 < 134 | 134 < 187 | 187 < 240 | 240 < 293 |2-13 Copyright © 2015 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.Chapter 02 - Descriptive Statistics: Tabular and Graphical Method2.20 a. (cont.) Frequency Distribution for Celebrity Annual Pay($mil) lower 28 81 134 187 240< < < < < <upper 81 134 187 240 293midpoint 54.5 107.5 160.5 213.5 266.5width 53 53 53 53 53frequency 17 6 0 1 1 25percent 34.0 12.0 0.0 2.0 2.0 50.0cumulative frequency 17 23 23 24 25cumulative percent 34.0 46.0 46.0 48.0 50.0Histogram of Pay ($mil) 18 16 14Frequency12 10 8 6 4 2 02881134 187 Pay ($mil)240293c. OgiveCumulative Percent100.075.050.025.00.0 2881134 187 Pay ($mil)240LO02-032-14 Copyright Š 2015 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.Chapter 02 - Descriptive Statistics: Tabular and Graphical Method2.21 a.The video game satisfaction ratings are concentrated between 40 and 46.b.Shape of distribution is slightly skewed left. Recall that these ratings have a minimum value of 7 and a maximum value of 49. This shows that the responses from this survey are reaching near to the upper limit but significantly diminishing on the low side.c.Class:Ratings: d.Cum Freq:1 34<x≤36 12 36<x≤38 43 38<x≤40 134 40<x≤42 255 42<x≤44 456 44<x≤46 617 46<x≤48 65LO02-03 2.22 a.The bank wait times are concentrated between 4 and 7 minutes.b.The shape of distribution is slightly skewed right. Waiting time has a lower limit of 0 and stretches out to the high side where there are a few people who have to wait longer.c.The class length is 1 minute.d.Frequency Distribution for Bank Wait Times lower -0.5 0.5 1.5 2.5 3.5 4.5 5.5 6.5 7.5 8.5 9.5 10.5 11.5< < < < < < < < < < < < < <upper 0.5 1.5 2.5 3.5 4.5 5.5 6.5 7.5 8.5 9.5 10.5 11.5 12.5midpoint 0 1 2 3 4 5 6 7 8 9 10 11 12width 1 1 1 1 1 1 1 1 1 1 1 1 1frequency 1 4 7 8 17 16 14 12 8 6 4 2 1 100percent 1% 4% 7% 8% 17% 16% 14% 12% 8% 6% 4% 2% 1%cumulative frequency 1 5 12 20 37 53 67 79 87 93 97 99 100cumulative percent 1% 5% 12% 20% 37% 53% 67% 79% 87% 93% 97% 99% 100%LO02-032-15 Copyright © 2015 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.Chapter 02 - Descriptive Statistics: Tabular and Graphical Method2.23 a.The trash bag breaking strengths are concentrated between 48 and 53 pounds.b.The shape of distribution is symmetric and bell shaped.c.The class length is 1 pound.d.Class: Cum Freq.46<47 47<48 48<49 49<50 50<51 51<52 52<53 53<54 54<55 2.5% 5.0% 15.0% 35.0% 60.0% 80.0% 90.0% 97.5% 100.0% OgiveCumulative Percent100.075.050.025.00.0 4547495153StrengthLO02-03 2.24 a.Because there are 30 data points, we will use 5 classes (Table 2.5). The class length will be (1700-304)/5= 279.2, rounded to the same level of precision as the data, 280. Frequency Distribution for MLB Team Value ($mil) lower 304 584 864 1144 1424< < < < <upper 584 864 1144 1424 1704midpoint 444 724 1004 1284 1564width 280 280 280 280 280frequency 24 4 1 0 1 30percent 80.0 13.3 3.3 0.0 3.3 100.0cumulative frequency 24 28 29 29 30cumulative percent 80.0 93.3 96.7 96.7 100.0Histogram of Value $mil 25Frequency20151050304584864 1144 Value $mil14241704Distribution is skewed right and has a distinct outlier, the NY Yankees.2-16 Copyright Š 2015 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.Chapter 02 - Descriptive Statistics: Tabular and Graphical Method2.24 b.Frequency Distribution for MLB Team Revenue lower 143 200 257 314 371< < < < <upper 200 257 314 371 428midpoint 171.5 228.5 285.5 342.5 399.5width 57 57 57 57 57frequency 16 11 2 0 1 30percent 53.3 36.7 6.7 0.0 3.3 100.0cumulative frequency 16 27 29 29 30cumulative percent 53.3 90.0 96.7 96.7 100.0Histogram of Revenues $mil 18 16 14Frequency12 10 8 6 4 2 0143200257 314 Revenues $mil371428The distribution is skewed right.c. Percent Frequency Polygon 100.0Percent80.0 60.0 40.0 20.0 0.0 304584864 1,144 Value ($mil)1,424LO02-032-17 Copyright Š 2015 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.Chapter 02 - Descriptive Statistics: Tabular and Graphical Method2.25 a.Because there are 40 data points, we will use 6 classes (Table 2.5). The class length will be (986-75)/6= 151.83. Rounding up to the same level of precision as the data gives a width of 152. Beginning with the minimum value for the first lower boundary, 75, add the width, 152, to obtain successive boundaries. Frequency Distribution for Sales ($mil) lower 75 227 379 531 683 835< < < < < <upper 227 379 531 683 835 987midpoint 151 303 455 607 759 911width 152 152 152 152 152 152frequency 9 8 5 7 4 7 40percent 22.5 20.0 12.5 17.5 10.0 17.5 100.0cumulative frequency 9 17 22 29 33 40cumulative percent 22.5 42.5 35.0 60.0 70.0 87.5Histogram of Sales ($mil) 99887Frequency776 5544 3 2 1 075227379531 Sales ($mil)683835987The distribution is relatively flat, perhaps mounded.2-18 Copyright Š 2015 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.Chapter 02 - Descriptive Statistics: Tabular and Graphical Method2.25 b.Again, we will use 6 classes for 40 data points. The class length will be (86-3)/6= 13.83. Rounding up to the same level of precision gives a width of 14. Beginning with the minimum value for the first lower boundary, 3, add the width, 14, to obtain successive boundaries. Frequency Distribution for Sales Growth (%) lower 3 17 31 45 59 73< < < < < <upper 17 31 45 59 73 87midpoint 10 24 38 52 66 80width 14 14 14 14 14 14frequency 5 15 13 4 2 1 40cumulative frequency 5 20 33 37 39 40percent 12.5 37.5 32.5 10.0 5.0 2.5 100.0cumulative percent 12.5 50.0 82.5 92.5 97.5 100.0Histogram of Sales Growth (%) 16151413Frequency12 10 8 65 4422 01 3173145 59 Sales Growth (%)7387The distribution is skewed right. LO02-032-19 Copyright Š 2015 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.Chapter 02 - Descriptive Statistics: Tabular and Graphical Method2.26 a.Frequency Distribution for Annual Savings in $000 lower 0 10 25 50 100 150 200 250 5002.26 b. andupper 10 25 50 100 150 200 250 500< < < < < < < <midpoint 5.0 17.5 37.5 75.0 125.0 175.0 225.0 375.0width 10 15 25 50 50 50 50 250frequency 162 62 53 60 24 19 22 21 37 460width =factor base 10 / 10 =1.0 15 / 10 =1.5 25 / 10 =2.5 50 / 10 =5.0 50 / 10 =5.0 50 / 10 =5.0 50 / 10 =5.0 250 / 10 =25.0frequency =height factor 162 / 1.0 =162.0 62 / 1.5 =41.3 53 / 2.5 =21.2 60 / 5.0 =12 24 / 5.0 =4.8 19 / 5.0 =3.8 22 / 5.0 =4.4 21 / 25.0 =0.82.27 Histogram of Annual Savings in $000160162150 140 130 120 110 100 90 80 70 60 50 4041.330 2021.21012.0 4.83.84.4 0.80102550100150200250500* 37Annual Savings ($000)LO02-032-20 Copyright Š 2015 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.Chapter 02 - Descriptive Statistics: Tabular and Graphical Method§2.3 CONCEPTS 2.28 The horizontal axis spans the range of measurements, and the dots represent the measurements. LO02-04 2.29 A dot plot with 1,000 points is not practical. Group the data and use a histogram. LO02-03, LO02-04§2.3 METHODS AND APPLICATIONS 2.30 DotPlot024681012AbsenceThe distribution is concentrated between 0 and 2 and is skewed to the right. Eight and ten are probably high outliers. LO02-04 2.31 DotPlot00.20.40.60.81RevgrowthMost growth rates are no more than 71%, but 4 companies had growth rates of 87% or more. LO02-04 2.32 DotPlot20253035404550556065HomersWithout the two low values (they might be outliers), the distribution is reasonably symmetric. LO02-042-21 Copyright © 2015 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.Chapter 02 - Descriptive Statistics: Tabular and Graphical Method§2.4 CONCEPTS 2.33 Both the histogram and the stem-and-leaf show the shape of the distribution, but only the stem-andleaf shows the values of the individual measurements. LO02-03, LO02-05 2.34 Several advantages of the stem-and-leaf display include that it: -Displays all the individual measurements. -Puts data in numerical order -Is simple to construct LO02-05 2.35 With a large data
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