© 2002 Thomson / South-Western Slide 2-1

Chapter 2

Descriptive Charts and

Graphs

© 2002 Thomson / South-Western Slide 2-2

Learning Objectives

• Construct a frequency distribution• Determine the class midpoints,

relative frequencies, and cumulative frequencies of a frequency distribution.

• Construct a histogram, a frequency polygon, an ogive, a pie chart.

© 2002 Thomson / South-Western Slide 2-3

Ungrouped vs Grouped Data

• Ungrouped data• have not been summarized in any

way• are also called raw data

• Grouped data• have been organized into a

frequency distribution

© 2002 Thomson / South-Western Slide 2-4

Example of Ungrouped Data

42

30

53

50

52

30

55

49

61

74

26

58

40

40

28

36

30

33

31

37

32

37

30

32

23

32

58

43

30

29

34

50

47

31

35

26

64

46

40

43

57

30

49

40

25

50

52

32

60

54

Ages of a Sample of Managers from Urban Child Care

Centers in theUnited States

© 2002 Thomson / South-Western Slide 2-5

Frequency Distribution of Child Care Manager’s Ages

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

© 2002 Thomson / South-Western Slide 2-6

Data Range

42

30

53

50

52

30

55

49

61

74

26

58

40

40

28

36

30

33

31

37

32

37

30

32

23

32

58

43

30

29

34

50

47

31

35

26

64

46

40

43

57

30

49

40

25

50

52

32

60

54

Smallest

Largest

Range = Largest - Smallest

= 74 - 23

= 51

© 2002 Thomson / South-Western Slide 2-7

Number of Classes and Class Width

• The number of classes should be between 5 and 15.• 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 approximate class width• Round up to a convenient number

10 = Width Class

8.5 =6

51 = Width Class eApproximat

© 2002 Thomson / South-Western Slide 2-8

Class Midpoint

Class Midpoint = beginning class endpoint + ending class endpoint

2

= 30 + 40

2= 35

Class Midpoint = class beginning point + 1

2class width

= 30 + 1

210

= 35

© 2002 Thomson / South-Western Slide 2-9

Relative Frequency RelativeClass Interval FrequencyFrequency20-under 30 6 .1230-under 40 18 .3640-under 50 11 .2250-under 60 11 .2260-under 70 3 .0670-under 80 1 .02 Total 50 1.00

6

50

18

50

© 2002 Thomson / South-Western Slide 2-10

Cumulative Frequency

CumulativeClass Interval Frequency Frequency20-under 30 6 630-under 40 18 2440-under 50 11 3550-under 60 11 4660-under 70 3 4970-under 80 1 50 Total 50

18 + 611 + 24

© 2002 Thomson / South-Western Slide 2-11

Class Midpoints, Relative Frequencies, and Cumulative Frequencies

Relative

CumulativeClass Interval Frequency Midpoint FrequencyFrequency20-under 30 6 25 .12 630-under 40 18 35 .36 2440-under 50 11 45 .22 3550-under 60 11 55 .22 4660-under 70 3 65 .06 4970-under 80 1 75 .02 50 Total 50 1.00

© 2002 Thomson / South-Western Slide 2-12

Cumulative Relative Frequencies

Cumulative Relative Cumulative RelativeClass Interval Frequency Frequency FrequencyFrequency20-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 1.00 Total 50 1.00

© 2002 Thomson / South-Western Slide 2-13

Common Statistical Graphs

• Histogram -- vertical bar chart of frequencies

• Frequency Polygon -- line graph of frequencies

• Ogive -- line graph of cumulative frequencies

• Pie Chart -- proportional representation for categories of a whole

© 2002 Thomson / South-Western Slide 2-14

Histogram

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

010

20

0 10 20 30 40 50 60 70 80

Years

Freq

uenc

y

© 2002 Thomson / South-Western Slide 2-15

Histogram Construction

Class Interval Frequency20-under 30 630-under 40 1840-under 50 1150-under 60 1160-under 70 370-under 80 1 0

1020

0 10 20 30 40 50 60 70 80

Years

Freq

uenc

y

© 2002 Thomson / South-Western Slide 2-16

Frequency Polygon

Class Interval Frequency20-under 30 630-under 40 1840-under 50 1150-under 60 1160-under 70 370-under 80 1 0

1020

0 10 20 30 40 50 60 70 80

Years

Fre

qu

ency

© 2002 Thomson / South-Western Slide 2-17

Ogive

CumulativeClass Interval Frequency20-under 30 630-under 40 2440-under 50 3550-under 60 4660-under 70 4970-under 80 50

02

04

06

00 10 20 30 40 50 60 70 80

Years

Fre

qu

en

cy

© 2002 Thomson / South-Western Slide 2-18

Relative Frequency Ogive

Cumulative

RelativeClass IntervalFrequency20-under 30 .1230-under 40 .4840-under 50 .7050-under 60 .9260-under 70 .9870-under 80 1.00

0.000.100.200.300.400.500.600.700.800.901.001.10

0 10 20 30 40 50 60 70 80

Years

Cu

mu

lati

ve R

elat

ive

Fre

qu

ency

© 2002 Thomson / South-Western Slide 2-19

Complaints by Amtrak PassengersComplaints by Amtrak Passengers

COMPLAINT NUMBER PROPORTION DEGREES

Stations, etc. 28,000 .40 144.0

TrainPerformance

14,700 .21 75.6

Equipment 10,500 .15 50.4

Personnel 9,800 .14 50.6

Schedules,etc.

7,000 .10 36.0

Total 70,000 1.00 360.0

© 2002 Thomson / South-Western Slide 2-20

Complaints by Amtrak PassengersComplaints by Amtrak Passengers

Stations, Etc.40%

Train Performance

21%

Equipment15%

Personnel14%

Schedules, Etc.10%

© 2002 Thomson / South-Western Slide 2-21

Second Quarter Truck Production in the U.S. (Hypothetical values)

2d QuarterTruck

ProductionCompany

A

B

C

D

ETotals

357,411

354,936

160,997

34,099

12,747920,190

© 2002 Thomson / South-Western Slide 2-22

39%39%

17%4%

1%

A B C D E

Second Quarter U.S. Truck Production

© 2002 Thomson / South-Western Slide 2-23

Pie Chart Calculations for Truck Producer Company A

2d QuarterTruck

ProductionProportion DegreesCompany

A

B

C

D

ETotals

357,411

354,936

160,997

34,099

12,747920,190

.388

.386

.175

.037

.0141.000

140

139

63

13

5360

357, 411

920,190 =

.388 360 =