Descriptive Statistics

Chapter 2

§ 2.2

More Graphs and Displays

Larson & Farber, Elementary Statistics: Picturing the World, 3e 3

Pie ChartA pie chart is a circle that is divided into sectors that represent categories. The area of each sector is proportional to the frequency of each category.

Accidental Deaths in the USA in 2002

(Source: US Dept. of Transportation) Continued.

Type Frequency

Motor Vehicle 43,500

Falls 12,200

Poison 6,400

Drowning 4,600Fire 4,200

Ingestion of Food/Object 2,900

Firearms 1,400

Larson & Farber, Elementary Statistics: Picturing the World, 3e 4

Pie Chart

To create a pie chart for the data, find the relative frequency (percent) of each category.

Continued.

TypeFrequen

cy

Relative Frequen

cy

Motor Vehicle 43,500 0.578

Falls 12,200 0.162

Poison 6,400 0.085

Drowning 4,600 0.061Fire 4,200 0.056

Ingestion of Food/Object

2,900 0.039

Firearms 1,400 0.019n = 75,200

Larson & Farber, Elementary Statistics: Picturing the World, 3e 5

Pie Chart

Next, find the central angle. To find the central angle, multiply the relative frequency by 360°.

Continued.

TypeFrequen

cy

Relative Frequen

cyAngle

Motor Vehicle 43,500 0.578 208.2°Falls 12,200 0.162 58.4°Poison 6,400 0.085 30.6°Drowning 4,600 0.061 22.0°Fire 4,200 0.056 20.1°Ingestion of Food/Object

2,900 0.039 13.9°

Firearms 1,400 0.019 6.7°

Larson & Farber, Elementary Statistics: Picturing the World, 3e 6

Pie Chart

Firearms1.9%

Motor vehicles57.8%

Poison8.5%

Falls16.2%

Drowning6.1%

Fire5.6%

Ingestion3.9%

Larson & Farber, Elementary Statistics: Picturing the World, 3e 7

Pareto Chart A Pareto chart is a vertical bar graph is which the height of each bar represents the frequency. The bars are placed in order of decreasing height, with the tallest bar to the left.

Accidental Deaths in the USA in 2002

(Source: US Dept. of Transportation) Continued.

Type Frequency

Motor Vehicle 43,500

Falls 12,200

Poison 6,400

Drowning 4,600Fire 4,200

Ingestion of Food/Object 2,900

Firearms 1,400

Larson & Farber, Elementary Statistics: Picturing the World, 3e 8

Pareto Chart

Accidental Deaths

5000

10000

35000

40000

45000

30000

25000

20000

15000

Pois

on

PoisonDrowningFallsMotor Vehicle

s

Fire Firearms

Ingestion of Food/Object

Larson & Farber, Elementary Statistics: Picturing the World, 3e 9

Scatter Plot

When each entry in one data set corresponds to an entry in another data set, the sets are called paired data sets. In a scatter plot, the ordered pairs are graphed as points in a coordinate plane. The scatter plot is used to show the relationship between two quantitative variables.

The following scatter plot represents the relationship between the number of absences from a class during the semester and the final grade.

Continued.

Larson & Farber, Elementary Statistics: Picturing the World, 3e 10

Scatter Plot

Absences Gradex

825

121596

y

78929058437481

Finalgrade

(y)

0 2 4 6 8 10 12 14 16

40

50

60

70

80

90

Absences (x)

100

From the scatter plot, you can see that as the number of absences increases, the final grade tends to decrease.

Larson & Farber, Elementary Statistics: Picturing the World, 3e 11

Making a Scatter plot

Height (inches) Weight (lbs)

76 200

70 185

68 170

69 175

70 200

65 160

66 160

67 175

71 205

74 215

Larson & Farber, Elementary Statistics: Picturing the World, 3e 12

Times Series Chart

A data set that is composed of quantitative data entries taken at regular intervals over a period of time is a time series. A time series chart is used to graph a time series. Example: The following table lists the number of minutes Robert used on his cell phone for the last six months.

Continued.

Month Minutes

January 236

February 242

March 188

April 175May 199

June 135

Construct a time series chart for the number of minutes used.

Larson & Farber, Elementary Statistics: Picturing the World, 3e 13

Times Series Chart

Robert’s Cell Phone Usage

200

150

100

50

250

0

Min

ute

s

Month

Jan Feb Mar Apr May June

Larson & Farber, Elementary Statistics: Picturing the World, 3e 14

Homework

Pages 532-6,all 8-14 even, 15, 18, 20, 22, 24, 26, 29, 30

Larson & Farber, Elementary Statistics: Picturing the World, 3e 15

Pages 56-59 - 1-2, 11-14, 16, 18, 21, 23, 25, 27

2 Unlike the histogram, the stem-and-leaf plot still contains the original data values. However, some data are difficult to organize in a stem-and-leaf plot.

12 The value of the stock portfolio has increased from around $5,000 in 2000 to almost $30,000 in 2004.

14 The most frequent incident occurring while driving and using a cell phone is swerving, twice as many people “sped up” than “cut off a car”

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Larson & Farber, Elementary Statistics: Picturing the World, 3e 17

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The greatest NASA space shuttle operations expenditures in 2003 were for vehicle and extravehicle activity while the least were for solid rocket booster.

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