Business Statistics

Chapter 2

Charts & Graphs& Graphs

SPby Ken Black

Learning Objectivesg j

• Recognize the difference betweengrouped and ungrouped data

• Construct a frequency distribution• Construct a histogram, a frequency

polygon, an ogive, a pie chart, a stemand leaf plot, a Pareto chart, and ascatter plotscatter plot

SP

Ungrouped Versus Grouped D tData

• Ungrouped data• have not been summarized in any wayy y• are also called raw data

• Grouped datap• have been organized into a frequency

distribution

SP

Example of Ungrouped Datap g p

42

30

26

58

32

37

34

50

57

30 Ages of a Sample of M f53

50

52

40

40

28

30

32

23

47

31

35

49

40

25

Managers from Tata Company

in India30

55

49

36

30

33

32

58

43

26

64

46

50

52

3249

61

74

33

31

37

43

30

29

46

40

43

32

60

54

SP

Frequency Distribution of Tata company Manager’s Agescompany Manager’s Ages

Class Interval Frequency20-under 30 620 under 30 630-under 40 1840-under 50 1140-under 50 1150-under 60 1160 under 70 360-under 70 370-under 80 1

SP

Data Range g

42

30

26

58

32

37

34

50

57

30Range = Largest - Smallest

= 74 - 2353

50

52

40

40

28

30

32

23

47

31

35

49

40

25

74 23= 51

30

55

49

36

30

33

32

58

43

26

64

46

50

52

32

Smallest49

61

74

33

31

37

43

30

29

46

40

43

32

60

54Largest

SP

Number of Classes and Class Width• The number of classes should be between 5 and 15.

• Fewer than 5 classes cause excessive summarization.Fewer than 5 classes cause excessive summarization.• More than 15 classes leave too much detail.

• Class Width• Divide the range by the number of classes for an• Divide the range by the number of classes for an

approximate class width• Round up to a convenient number

8.5=51Range=WidthClasseApproximat =

10 = Width Class

8.56IntervalClassofNo.

Width Class eApproximat

SP

Class Midpointp

Class Midpoint = beginning class endpoint + ending class endpoint

22

= 30 + 40

2= 35= 35

Class Midpoint = class beginning point + 12

class width

( )

2

= 30 + 12

10

= 35

SP

35

Relative Frequencyq yRelative

Class Interval Frequency Frequencyq y q y20-under 30 6 .1230-under 40 18 .36

650

=30 under 40 18 .3640-under 50 11 .2250-under 60 11 22

50

1850

=50-under 60 11 .2260-under 70 3 .0670 under 80 1 02

50

70-under 80 1 .02Total 50 1.00

SP

Cumulative Frequencyq yCumulativeCumulative

Cl I t lCl I t l FF FFClass IntervalClass Interval FrequencyFrequency FrequencyFrequency2020--under 30under 30 66 663030--under 40under 40 1818 242418 + 63030--under 40under 40 1818 24244040--under 50under 50 1111 35355050--under 60under 60 1111 4646

18 + 611 + 24

6060--under 70under 70 33 49497070--under 80under 80 11 5050

TotalTotal 5050

SP

Class Midpoints, Relative Frequencies, p qand Cumulative Frequencies

RelativeRelative CumulativeCumulativeClass IntervalClass Interval FrequencyFrequency MidpointMidpoint FrequencyFrequency FrequencyFrequencyq yq y pp q yq y q yq y2020--under 30under 30 66 2525 .12.12 663030--under 40under 40 1818 3535 .36.36 24244040--under 50under 50 1111 4545 2222 35354040--under 50under 50 1111 4545 .22.22 35355050--under 60under 60 1111 5555 .22.22 46466060--under 70under 70 33 6565 .06.06 49497070 d 80d 80 11 7575 0202 50507070--under 80under 80 11 7575 .02.02 5050

TotalTotal 5050 1.001.00

SP

Cumulative Relative Frequenciesq

CumulativeCumulativeRelative Cumulative Relative

Class Interval Frequency Frequency Frequency Frequency20 d 30 6 12 6 1220-under 30 6 .12 6 .1230-under 40 18 .36 24 .4840-under 50 11 .22 35 .7050-under 60 11 .22 46 .9260-under 70 3 .06 49 .9870-under 80 1 .02 50 1.0070 under 80 1 .02 50 1.00

Total 50 1.00

SP

Common Statistical Graphsp

• Histogram -- vertical bar chart of frequencies• Frequency Polygon -- line graph of frequencies• Ogive -- line graph of cumulative frequencies• Pie Chart -- proportional representation for

i f h lcategories of a whole• Stem and Leaf Plot

P• Pareto• Scatter Plot

SP

Histogramg

Class Interval Frequency20-under 30 6

20

30-under 40 1840-under 50 11 10qu

ency

50-under 60 1160-under 70 370 d 80 1

Freq

70-under 80 1 0

0 10 20 30 40 50 60 70 80

Years

SP

Histogram Constructiong

Class IntervalClass Interval FrequencyFrequency2020--under 30under 30 66 20

3030--under 40under 40 18184040--under 50under 50 1111

0ency

5050--under 60under 60 11116060--under 70under 70 337070 d 80d 80 11

10

Freq

ue

7070--under 80under 80 110

0 10 20 30 40 50 60 70 80

SP

Years

Frequency Polygonq y yg

Class Interval Frequency20-under 30 6

20

30-under 40 1840-under 50 11

10quen

cy50-under 60 1160-under 70 370 d 80 1

Freq

70-under 80 1 0

0 10 20 30 40 50 60 70 80

Years

SP

ea s

OgiveOgive

CumulativeClass Interval Frequency 60

20-under 30 630-under 40 2440 d 50 35

40

eque

ncy

40-under 50 3550-under 60 4660 under 70 49 0

20Fre

60-under 70 4970-under 80 50

0

0 10 20 30 40 50 60 70 80

Years

SP

Relative Frequency OgiveRelative Frequency Ogive

C m lati eCumulativeRelative

Class Interval Frequency 0.901.00

uenc

y

Class Interval Frequency20-under 30 .1230-under 40 .48

0 400.500.600.700.80

elat

ive

Freq

u40-under 50 .7050-under 60 .92

0 000.100.200.300.40

umul

ativ

e R

e

60-under 70 .9870-under 80 1.00

0.000 10 20 30 40 50 60 70 80

Years

Cu

SP

Pie ChartPie Chart

Class Interval Frequency Midpoint Relative Frequency

20‐under 30 25 6 0.12 15

62%

Relative Frequency

30‐under 40 35 18 0.36

40‐under 50 45 11 0.22

12%4

22%

6%

50‐under 60 55 11 0.22

60‐under 70 65 3 0.06

236%

370‐under 80 75 1 0.02

50 1

322%

SP

Safety Examination Scores yfor Plant Trainees

86 77 91 60 55

Raw Data Stem

2

Leaf

386

76

23

92

59

9

47

72

60

88

75

55

67

83

2

3

4

3

9

7 9 23

77

81

59

68

75

72

82

74

75

97

39

83

89

67

5

6

5 6 9

0 7 7 8 881

79

68

75

83

49

74

70

56

39

78

94

67

91

81

7

8

9

0 2 4 5 5 6 7 7 8 9

1 1 2 3 3 6 8 9

1 1 2 4 7

SP

68 49 56 94 81 9 1 1 2 4 7

Construction of Stem and Leaf Plot

86 77 91 60 55

Raw Data Stem

2

Leaf

3Stem

76

23

92

59

47

72

88

75

67

83

3

4

5

9

7 9

5 6 9

Stem

77

81

68

75

82

74

97

39

89

67

5

6

7

5 6 9

0 7 7 8 8

0 2 4 5 5 6 7 7 8 9Leaf

St79

68

83

49

70

56

78

94

91

81

8

9

1 1 2 3 3 6 8 9

1 1 2 4 7

Stem

Leaf

SP

Pareto ChartPareto Chart

Pareto chart is a graphical technique of displaying ag p q p y g

problem cause.

It is a special type of vertical bar chart in which theIt is a special type of vertical bar chart in which the

categorized responses are plotted in the descending rank

d f th i f i d bi d ithorder of their frequencies and combined with a

cumulative polygon on the same graph.

The main focus of the Pareto chart is to separate the “very

important” from the “unimportant.”

Pareto Chart : Taj Hotel Group conducted a customer satisfaction survey of 340customers who attended a special dinner arranged at the hotel. The survey groupprepared a questionnaire that was divided in two parts: satisfaction reasons anddissatisfaction reasons. Taj Hotel Group has decided to focus on the reasons ofdissatisfaction rather than on satisfaction factors to improve its quality of service.dissatisfaction rather than on satisfaction factors to improve its quality of service.The following observations regarding categories of dissatisfaction were made(Table 2.9).

Sr.No Dissatisfaction Reasons Customers1 Poor Service 902 Quality of Food 1103 Time taken in placing an order 404 Dull music arrangement 504 Dull music arrangement 505 Late intimation of dinner program 306 Parking Facility 20

340340

Scatter PlotScatter Plot

The scatter plot is a graphical presentation of thep g p p f

relationship between two numerical variables.

It generally shows the nature of the relationship between twoIt generally shows the nature of the relationship between two

variables.

The application of a scatter plot is very common inThe application of a scatter plot is very common in

regression, multiple regressions, correlation, etc.

SP

Scatter Plot : Chhattisgarh become a new state in 2000. The property prices in the statecapital, Raipur, are zooming up. The real estate business has an edge over other businessstreams. Bhilai, an important industrial town of Chhattisgarh is also experiencing the samephenomenon Table 2 10 shows the escalation of property prices (average price in majorphenomenon. Table 2.10 shows the escalation of property prices (average price in majorlocations) in Raipur and Bhilai in the past 7 years in different quarters. From Table 2.10,construct a scatter plot. Figures are in rupees per square feet.

T bl 2 10Table 2.10

Figure 2.54 : Scatter plot for the data given in Table 2.10 (Example g p f g ( p2.8)

A X company surveyed age of 53 of its middle level Whi h h l b i d imanagers. Which has later been organised into

frequency distribution as shown below. Determine the class midpoint relative frequency & Cum R F forclass midpoint, relative frequency & Cum. R.F for

these data. Compute a histogram, frequency polygon, Ogive & Pie chart for the same. g

CI F20-25 825-30 630-35 530 35 535-40 1240-45 1545 50 7

SP

45-50 7

Th k UThank U

SP