Statistics - Describing Data I

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Lecture 2: Describing Data ILecture 2: Describing Data I

GOALS

ONE

Organize data into a frequency distribution.TWO

Portray a frequency distribution in a histogram, frequency polygon, and

cumulative frequency polygon.

THREE

Develop a stem-and-leaf display.

FOUR

Present data using such graphic techniques as line charts, bar charts,

and pie charts.


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EXAMPLE 1EXAMPLE 1

Dr. Jame is Dean of the School of Business NationalUniversity. He wishes prepare to a report showingthe number of hours per week students spendstudying. He selects a random sample of 30 students

and determines the number of hours each studentstudied last week.

15.0, 23.7, 19.7, 15.4, 18.3, 23.0, 14.2, 20.8, 13.5,

20.7, 17.4, 18.6, 12.9, 20.3, 13.7, 21.4, 18.3, 29.8,17.1, 18.9, 10.3, 26.1, 15.7, 14.0, 17.8, 33.8, 23.2,12.9, 27.1, 16.6.


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Frequency DistributionFrequency Distribution

AFrequency distribution is a grouping of data

into mutually exclusive categories showing the

number of observations in each class.


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Example 1Example 1 continuedcontinued

Estimate the number of classes.

There are 30 observations. 2>30.We should have at

least 5 classes.

Find Range (R ) to determine class width

The range is 23.5 hours. Choose an interval of 5

hours.

Set the first lower limit.The lower limit of the first class is 7.5 hours.

Count the number of values in each class and fill in

the table.


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ExampleExample 11 continuedcontinued

Hours Frequency (f)

7.5 up to 12.5 1

12.5 up to 17.5 12

17.5 up to 22.5 10

22.5 up to 27.5 5

27.5 up to 32.5 1

32.5 up to 37.5 1

Total 30


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Frequency Distribution TerminologyFrequency Distribution Terminology

Class midpoint:

A point that divides a class into two equal parts. This isthe average of the upper and lower class limits.

Class frequency:

The number of observations in each class.

Class interval:

The class interval is obtained by subtracting the lowerlimit of a class from the lower limit of the next class.


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A relative frequency distribution shows the

proportion of observations in each class.


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Relative Frequency DistributionRelative Frequency Distribution

Hours Frequency (f) Relative Frequency

7.5 up to 12.5 1 1/30 = 0.0333

12.5 up to 17.5 12 12/30 = 0.4000

17.5 up to 22.5 10 10/30 = 0.3330

22.5 up to 27.5 5 5/30 = 0.1667

27.5 up to 32.5 1 1/30 = 0.0333

32.5 up to 37.5 1 1/30 = 0.0333

Total 30 30/30 = 1.0000


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EXAMPLEEXAMPLE 22

Colin achieved the following scores on his twelve

accounting quizzes this semester:

86, 79, 92, 84, 69, 88, 91, 83, 96, 78, 82, 85.

Organize this data to show its distribution.

69, 78, 79, 82, 83, 84, 85, 86, 88, 91, 92, 96

12 data, so recommend at least 4 classes

Range = 96-69 = 27. Class width = 7

66-73, 73-80, 80- 87, 87-94, 94-101


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StemStem--andand--leaf Displaysleaf Displays

Stem-and-leaf display: A statistical techniquefor displaying a set of data. Each numericalvalue is divided into two parts: the leading

digits become the stem and the trailing digitsthe leaf.

Note: an advantage of the stem-and-leaf

display over a frequency distribution is we donot lose the identity of each observation.


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stem lea

6 9

7 8 9

8 2 3 4 5 6 8

9 1 2 6



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Graphic Presentation of a FrequencyGraphic Presentation of a Frequency

DistributionDistributionThe three commonly used graphic forms are histograms,

frequency polygons, and a cumulative frequency

distribution.

A Histogram is a graph in which the classes aremarked on the horizontal axis and the class

frequencies on the vertical axis.

The class frequencies are represented by the

heights of the bars and the bars are drawn adjacent

to each other.


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Graphic Presentation of a FrequencyGraphic Presentation of a Frequency

DistributionDistribution

A frequency polygon consists of line segments

connecting the points formed by the class midpoint

and the class frequency.

A cumulative frequency distribution is used to

determine how many or what proportion of the datavalues are below or above a certain value.


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Histogram for Hours Spent StudyingHistogram for Hours Spent Studying

0

2

4

6

8

10

12

14

10 15 20 25 30 35

Hours spent studying

requenc

y


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Frequency Polygon for Hours SpentFrequency Polygon for Hours Spent

StudyingStudying

0

2

4

6

810

12

14

10 15 20 25 30 35

H r t t y

Fr

y


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Cumulative Frequency Distribution forCumulative Frequency Distribution forHours StudyingHours Studying

0

5

10

15

20

25

30

35

10 15 20 25 30 35

Hours e t tudyi

re ue cy


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OtherGraphic Presentations of DataOtherGraphic Presentations of Data

Line chart is useful for showing the trends of the

data over time.

Bar Chart is useful for displaying the difference

between group of data.

Pie chart is useful for displaying a relative

frequency distribution among group of data.


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ExampleExample 33

Construct a graphical presentation for the number

of unemployed per 100,000 population for

selected cities during 2001.


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ExampleExample33

Cities Number of Unemployed

per 100, 000 population

Atlanta, GA 7,300

Boston,MA 5,400

Chicago, IL 6,700

LosAngeles, CA 8,900

New York, NY 8,200

Washington, D.C. 8,900


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Bar Chart for the Unemployment DataBar Chart for the Unemployment Data

7300

5400

6700

89008200

8900

0

2000

4000

6000

8000

10000

1 2 3 4 5 6

Cities

#unemployed/

100,0

00

Atl taBoston

Chi ago

Los Angeles

New York

Wash

ington


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EXAMPLEEXAMPLE 44

A sample of 200 runners were asked to indicate

their favorite type of running shoe. Draw a

graphical presentation for this data.

Types of Shoe The number of runners

Nike 92

Adidas 49

Reebok 37

Asics 13

Other 9


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Pie Chart for Running ShoesPie Chart for Running Shoes

Nik

A i as

okAsi s

Other

Nike

A i as

Reebok

Asi s

Other


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ExercisesExercises

AIN is a leader the in logistic business. The following data is its

annual report for primary net income per common share for years1999 to 2004.

1999 2000 2001 2002 2003

$0.50 $0.62 $1.03 $1.37 $1.34

What kind of graphical tool should be used to present this data?

Line Graph


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ExercisesExercises

The following information report the companys consumer sales (inmillions) by region.

Region Sales

Americas 574.50Europe 486.70

Asian/Pacific 86.10

What kind of graphical tool should be used to present this data?

Bar Chart or Pie Chart


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ExercisesExercises

Based on the previous exercise, which graphical tool between bar

chart and pie chart is better describes the relative proportion of thetotal sales?

Pie Chart


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HomeworkHomework

Chapter 2:

Problems: 10, 12, 14, 27, 28, and 48

Chapter 4:

Problems: 8

Documents

Statistics - Describing Data I