ken black solution chapter 2

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Chapter 2: Charts and Graphs 1

Chapter 2Charts and Graphs

LEARNING OBJECTIVES

The overall objective of chapter 2 is for you to master several techniques forsummarizing and depicting data, thereby enabling you to:

1. Recognize the difference between grouped and ungrouped data.

2. Construct a frequency distribution.

3. Construct a histogram, a frequency polygon, an ogive, a pie chart, a stem and leafplot, a Pareto chart, and a scatter plot.

CHAPTER TEACHING STRATEGY

Chapter 1 brought to the attention of students the wide variety and amount of dataavailable in the world of business. In chapter 2, we confront the problem of trying tobegin to summarize and present the data in a meaningful manner. One mechanism fordata summarization is the frequency distribution which is essentially a way of organizingungrouped or raw data into grouped data. It is important to realize that there isconsiderable art involved in constructing a frequency distribution. There are nearly asmany possible frequency distributions for a problem as there are students in a class.Students should begin to think about the receiver or user of their statistical product. Forexample, what class widths and class endpoints would be most familiar and meaningfulto the end user of the distribution? How can the data best be communicated andsummarized using the frequency distribution?

The second part of chapter 2 presents various ways to depict data using graphs.The student should view these graphical techniques as tools for use in communicatingcharacteristics of the data in an effective manner. Most business students will have sometype of management opportunity in their field before their career ends. The ability tomake effective presentations and communicate their ideas in succinct, clear ways is anasset. Through the use of graphics packages and such techniques as frequency polygons,


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ogives, histograms, and pie charts, the manager can enhance his/her personal image as acommunicator and decision-maker. In addition, emphasize that the final product (thefrequency polygon, etc.) is just the beginning. Students should be encouraged to studythe graphical output to recognize business trends, highs, lows, etc. and realize that theultimate goal for these tools is their usage in decision making.

CHAPTER OUTLINE

2.1 Frequency DistributionsClass MidpointRelative FrequencyCumulative Frequency

2.2 Graphic Depiction of DataHistograms

Frequency PolygonsOgivesPie ChartsStem and Leaf PlotsPareto Charts

2.3 Graphical Depiction of Two-Variable Numerical Data: Scatter Plots

KEY TERMS

Class Mark Pareto ChartClass Midpoint Pie ChartCumulative Frequency RangeFrequency Distribution Relative FrequencyFrequency Polygon Scatter PlotGrouped Data Stem and Leaf PlotHistogram Ungrouped DataOgive

SOLUTIONS TO PROBLEMS IN CHAPTER 2

2.1a) One possible 5 class frequency distribution:

Class Interval Frequency10 - under 25 925 - under 40 1340 - under 55 11


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55 - under 70 970 - under 85 8

50

b) One possible 10 class frequency distribution:

Class Interval Frequency10 - under 18 718 - under 26 326 - under 34 534 - under 42 942 - under 50 750 - under 58 358 - under 66 666 - under 74 474 - under 82 4

82 - under 90 2

c) The ten class frequency distribution gives a more detailed breakdown oftemperatures, pointing out the smaller frequencies for the higher temperatureintervals. The five class distribution collapses the intervals into broaderclasses making it appear that there are nearly equal frequencies in each class.

2.2 One possible frequency distribution is the one below with 11 classes and classintervals of 2.

Class Interval Frequency39 - under 41 241 - under 43 143 - under 45 545 - under 47 1047 - under 49 1849 - under 51 1351 - under 53 1553 - under 55 1555 - under 57 757 - under 59 959 - under 61 2

The distribution reveals that only 13 of the 100 boxes of raisins contain 50 1raisin (49 -under 51). However, 71 of the 100 boxes of raisins contain between45 and 55 raisins. It shows that there are a few boxes (5) that have 9 or moreextra raisins (59-61) and two boxes that have 9-11 less raisins (39-41) than theboxes are supposed to contain.

2.3Class Class Relative Cumulative


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Interval Frequency Midpoint Frequency Frequency0 - 5 6 2.5 6/86 = .0698 65 - 10 8 7.5 .0930 14

10 - 15 17 12.5 .1977 3115 - 20 23 17.5 .2674 54

20 - 25 18 22.5 .2093 7225 - 30 10 27.5 .1163 8230 - 35 4 32.5 .0465 86

TOTAL 86 1.0000

The relative frequency tells us that it is most probable that a customer is in the15 - 20 category (.2674). Over two thirds (.6744) of the customers are between 10and 25 years of age.

2.4Class Class Relative Cumulative

Interval Frequency Midpoint Frequency Frequency0-2 218 1 .436 2182-4 207 3 .414 4254-6 56 5 .112 4816-8 11 7 .022 4928-10 8 9 .016 500

TOTAL 500 1.0000

2.5 Some examples of cumulative frequencies in business:

sales for the fiscal year,costs for the fiscal year,spending for the fiscal year,inventory build-up,accumulation of workers during a hiring buildup,production output over a time period.

2.6 Histogram


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Frequency Polygon

2.7 Histogram


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Frequency Polygon

2.8 Ogive


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2.9

STEM LEAF

21 2, 8, 8, 922 0, 1, 2, 4, 6, 6, 7, 9, 923 0, 0, 4, 5, 8, 8, 9, 9, 9, 924 0, 0, 3, 6, 9, 9, 925 0, 3, 4, 5, 5, 7, 7, 8, 926 0, 1, 1, 2, 3, 3, 5, 627 0, 1,

2.10 Company Proportion Degrees

Andersen Worldwide .25 90Ernst & Young .20 72Deloitte & Touche .17 61KPMG Peat Marwick .12 43Coopers & Lybrand .11 40Price Waterhouse .11 40Grant Thornton .01 4McGladrey & Pullen .01 4

BDO Seidman .01 4

TOTAL .99 358

Pie Chart


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2. 11 Company Proportion Degrees

Delta .27 97United .22 79American .21 76US Airways .15 54Southwest .15 54

TOTAL 1.00 360

2.12

Brand Proportion Degrees


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Huggies .413 149Pampers .256 92Luvs .121 44Drypers .033 12

Fitti .009 3Private Labels .158 57

TOTAL .990 357

Pie Chart

2.13 STEM LEAF

1 3, 6, 7, 7, 7, 9, 9, 92 0, 3, 3, 5, 7, 8, 9, 93 2, 3, 4, 5, 7, 8, 84 1, 4, 5, 6, 6, 7, 7, 8, 8, 95 0, 1, 2, 2, 7, 8, 9

6 0, 1, 4, 5, 6, 7, 97 0, 78 0

The stem and leaf plot shows that the number of passengers per flight wererelatively evenly distributed between the high teens through the sixties. Rarelywas there a flight with at least 70 passengers. The category of 40's contained themost flights (10).


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2.14 Complaint Number % of Total

Busy Signal 420 56.45Too long a Wait 184 24.73Could not get through 85 11.42

Get Disconnected 37 4.97Transferred to the Wrong Person 10 1.34Poor Connection 8 1.08Total 744 99.99

2.15

0

500

1000

1500

2000

2500

3000

3500

0 1000 2000 3000 4000 5000 6000 7000

Human Food

IndustrialProducts


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2.16

0

20

40

60

80

100

120

140

160

180

0 2 4 6 8 10 12

Advertising

Sales

2.17Class Interval Frequencies

16 - under 23 623 - under 30 930 - under 37 4


TOTAL 30

2.18Class Interval Frequency Midpoint Rel.Freq. Cum.Freq.

20 - under 25 17 22.5 .207 .20725 - under 30 20 27.5 .244 .451

30 - under 35 16 32.5 .195 .64635 - under 40 15 37.5 .183 .82940 - under 45 8 42.5 .098 .92745 - under 50 6 47.5 .073 1.000


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2.19 Class Interval Frequencies


80 - under 90 3190 - under 100 9

TOTAL 123

Histogram

Frequency Polygon


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Ogive

2.20Label Value Proportion Degrees

A 55 .180 65B 121 .397 143C 83 .272 98D 46 .151 54

TOTAL 305 1.000 360

Pie Chart


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2.21

STEM LEAF

28 4, 6, 929 0, 4, 830 1, 6, 8, 931 1, 2, 4, 6, 7, 732 4, 4, 633 5

2.22 Problem Frequency Percent of Total

1 673 26.96

2 29 1.163 108 4.334 379 15.185 73 2.926 564 22.607 12 0.488 402 16.119 54 2.16

10 202 8.092496

Pareto Chart:


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2.23

0

2

4

6

8

10

12

14

16

0 2 4 6 8 10 12 14 16 18

X

Y

2.24 Olson Company

Frequency distribution

Class Interval Frequency

32 - under 37 137 - under 42 442 - under 47 1247 - under 52 1152 - under 57 1457 - under 62 562 - under 67 267 - under 72 1

TOTAL 50


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2.25Class Class Relative CumulativeInterval Frequency Midpoint Frequency Frequency

20 25 8 22.5 8/53 = .1509 825 30 6 27.5 .1132 1430 35 5 32.5 .0943 1935 40 12 37.5 .2264 340 45 15 42.5 .2830 4645 50 7 47.5 .1321 53TOTAL 53 .9999

2.26 Frequency Distribution:

Class Interval Frequency

10 - under 20 220 - under 30 330 - under 40 940 - under 50 750 - under 60 1260 - under 70 970 - under 80 680 - under 90 2

50

Histogram


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Frequency Polygon

The normal distribution appears to peak near the center and diminish towards theend intervals.

2.27

a) Histogram and a Frequency Polygon for 2.25

Class CumulativeInterval Frequency Frequency20 - 25 8 825 - 30 6 1430 - 35 5 1935 - 40 12 3140 - 45 15 4645 - 50 7 53TOTAL 53


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Histogram

Frequency Polygon


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b) Ogive

2.28Cumulative

Asking Price Frequency Frequency

$ 60,000 - under $ 70,000 21 21$ 70,000 - under $ 80,000 27 48$ 80,000 - under $ 90,000 18 66$ 90,000 - under $100,000 11 77$100,000 - under $110,000 6 83$110,000 - under $120,000 3 86

86


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Histogram

Frequency Polygon


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Ogive

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Amount Spent Cumulativeon Prenatal Care Frequency Frequency

$ 0 - under $100 3 3$100 - under $200 6 9$200 - under $300 12 21$300 - under $400 19 40$400 - under $500 11 51$500 - under $600 6 57

57


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Histogram

Frequency Polygon


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Ogive

2.30Cumulative

Price Frequency Frequency

$1.75 - under $1.90 9 9$1.90 - under $2.05 14 23$2.05 - under $2.20 17 40$2.20 - under $2.35 16 56$2.35 - under $2.50 18 74$2.50 - under $2.65 8 82$2.65 - under $2.80 5 87

87


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Histogram

Frequency Polygon


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Ogive

2.31

Genre Albums Sold Proportion Degrees

R&B 146.4 .29 104Alternative 102.6 .21 76Rap 73.7 .15 54Country 64.5 .13 47Soundtrack 56.4 .11 40Metal 26.6 .05 18Classical 14.8 .03 11Latin 14.5 .03 11

TOTAL 1.00 361


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Pie Chart

2.32

0

100

200

300

400

500

600

700

0 5 10 15 20 25 30 35

Agricultural Products


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2.33

Industry Total Release Proportion Degrees

Chemicals 737,100,000 .37 133

Primary metals 566,400,000 .28 101Paper 229,900,000 .11 40Plastics & Rubber 109,700,000 .05 18Transportation

Equipment 102,500,000 .05 18Food 89,300,000 .04 14Fabricated Metals 85,900,000 .04 14Petroleum 63,300,000 .03 11Electrical

Equipment 29,100,000 .01 4

TOTAL 0.98 353

Pie Chart

Chemicals38%

Primary Metals

29%

Paper

11%

Plas. & Rubber

5%

Transpor tation Equipment

5%

Food

4%

Fab. Metals

4%

Petroleum

3%

Elec. Equip.

1%

2.34


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Discolorat

ion

Labeling

BrokenHan

dle

Thicknes

s

FaultinPla

stic

324486117221

6.48.817.223.444.2

100.093.684.867.644.2

500

400

300

200

100

0

100

80

60

40

20

0

Defect

Count

Percent

Cum %

Percent

Count

Problem 2.34

2.35STEM LEAF

42 12, 16, 24, 32, 99, 99

43 04, 28, 39, 46, 61, 8844 20, 40, 5945 1246 53, 5447 30, 34, 5848 22, 34, 66, 7849 6350 48, 49, 9051 6652 21, 54, 57, 63, 9153 38, 66, 66

54 31, 7855 5656 6957 37, 5058 31, 32, 58, 7359 19, 23

2.36


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STEM LEAF

22 00, 6823 01, 37, 44, 7524 05, 37, 48, 60, 68

25 24, 5526 02, 56, 70, 7727 42, 60, 6428 14, 3029 22, 61, 75, 76, 90, 9630 02, 10

2.37 The distribution of household income is bell-shaped with an average of about $

90,000 and a range of from $ 30,000 to $ 140,000.

2.38 Family practice is most prevalent with about 20% with pediatrics next at slightlyless. A virtual tie exists between ob/gyn, general surgery, anesthesiology, andpsychiatry at about 14% each.

2.39 The fewest number of audits is 12 and the most is 42. More companies (8)performed 27 audits than any other number. Thirty-five companies performedbetween 12 and 19 audits. Only 7 companies performed 40 or more audits.

2.40 There were relatively constant sales from January through August ($4 to 6 million).Each month from September through December sales increased with Decemberhaving the sharpest increase ($15 million in sales in December).

ken black solution chapter 2

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