ns2 data presenting 14

7/24/2019 NS2 Data Presenting 14

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Chapter 2Presenting Data in

Tables and Charts

David Chow

Sep 2014


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A Picture Is Worth a Thousand Words


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Categorical Data


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Organizing Categorical Data:

Summary Table A summary table indicates the frequency, amount, or

percentage of items in a set of categories.

You can easily see differences between categories.

How do you spend the holidays? Percent

At home with family 45%

Travel to visit family 38%

Vacation 5%Catching up on work 5%

Other 7%


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Bar Chart & Pie Chart In a bar chart, a bar

shows each category, thelength of which

represents the amount,frequency or percentage.

How Do You Spend the Holidays?

45%

38%

5%

5%

7%

0% 10% 20% 30% 40% 50%

At home w ith family

Travel to visit family

Vacation

Catching up on w ork

Other

Pie chart is a circlebroken up into slicesrepresenting categories.

The size of each slice

corresponds to thepercentage share.

How Do You Spend the Holiday's

45%

38%

5%

5%7%

At home with family

Travel to visit family

Vacation

Catching up on work

Other


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Pareto Diagram Also for categorical data

Essentially, it is a bar chart and a cumulative

polygon in the same graph

Categories are shown in descending order of frequency

Easy to see the vital few versus the trivial many


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Pareto Diagram

cumulative%invested

(linegraph)

%i

nves

tedineach

category

(bargraph)

0%

5%

10%

15%

20%

25%

30%

35%

40%

45%

Stocks Bonds Savings CD

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

Current Investment Portfolio Pareto diagram

is a bar chart &

a cumulativepolygon together

- in descendingorder offrequency

- easy to see thevital few


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Numerical DataOrdered Array & Stem-

and-Leaf


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Organizing Numerical Data:

Ordered Array An ordered array is a sequence of data, in rank order, from

the smallest value to the largest value.

Age ofSurveyed

College

Students

Day Students16 17 17 18 18 18

19 19 20 20 21 22

22 25 27 32 38 42

Night Students

18 18 19 19 20 21

23 28 32 33 41 45


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Stem and Leaf Display A stem-and-leaf display organizes data into groups (called

stems) so that the values within each group (the leaves)

branch out to the right on each row.

Stem Leaf

1 67788899

2 0012257

3 28

4 2

Age of College Students (stem: 10s column)

Day Students Night Students

Stem Leaf

1 8899

2 0138

3 23

4 15


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Stem-and-Leaf Display

Construct a stem-and-leaf display forthe following data sets:

1. Midterm scores: 50, 74, 74, 76, 81

2. Average daily expenditure:

$36.15, $31.00, $35.05, $40.25, $33.75


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Numerical Data:Tables & Charts


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Frequency Distribution The frequency distribution is a summary table in which the

data are arranged into numerically ordered class groupings.

You must give attention to selecting the appropriate number ofclass groupings, determining a suitable width of a classgrouping, and establishing the boundaries of each to avoidoverlapping.

To determine the width of a class interval, you divide therange (highest value - lowest value) by the number of classgroupings desired.


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Frequency Distribution Example

Example: A manufacturer of insulation randomly selects 20

winter days and records the daily high temperature (in

Fahrenheit):

24, 35, 17, 21, 24, 37, 26, 46, 58, 30, 32, 13, 12, 38, 41, 43, 44, 27, 53, 27


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Frequency Distribution Example Sort raw data in ascending order:

12, 13, 17, 21, 24, 24, 26, 27, 27, 30, 32, 35, 37, 38, 41, 43, 44, 46, 53, 58

Find range: 58 - 12 = 46

Select number of classes: 5 (usually between 5 and 15)

Compute class interval (width): 10 (46/5 then round up)

Determine class boundaries (limits): 10, 20, 30, 40, 50, 60

Compute class midpoints: 15, 25, 35, 45, 55

Count observations & assign to classes


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Frequency Distribution Example

Class Frequency

10 but less than 20 3 .15 15

20 but less than 30 6 .30 30

30 but less than 40 5 .25 25

40 but less than 50 4 .20 20

50 but less than 60 2 .10 10

Total 20 1.00 100

RelativeFrequency

Percentage


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The Histogram The graphical version of a frequency distribution is

called a histogram.

The class boundaries(or class midpoints) areshown on the horizontal axis. The vertical axis can

be frequency, relative frequency, orpercentage.

Bars of the appropriate heights are used to representthe number of observations within each class.


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The Histogram

Class Frequency

10 but less than 20 3 .15 15

20 but less than 30 6 .30 30

30 but less than 40 5 .25 25

40 but less than 50 4 .20 20

50 but less than 60 2 .10 10

Total 20 1.00 100

RelativeFrequency

Percentage

Histogram: Daily High Temperature

0

1

2

3

4

5

6

7

5 15 25 35 45 55 More

Frequency


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Histogram in Excel: Step 1

Earlier Versions

Select Tools/Data Analysis

EXCEL 2010 VersionData > Data Analysis*

You may need to activate Data Analysis

by yourself. Simply click

File > Options > Add-in


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Histogram in Excel: Steps 2-4

2. Choose Histogram

3. Input data range and binrange (bin range is a cell rangecontaining the upper class boundariesfor each class grouping)

4. Select Chart Output

and click OK


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The Polygon A percentage polygon is formed by having the

midpoint of each class represent the data in that class

and then connecting the sequence of midpoints at

their respective class percentages.

The cumulative percentage polygon, or ogive,

displays the variable of interest along theX

axis, andthe cumulative percentages along the Y axis.


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The Polygon

Frequency Polygon: Daily High Temperature

0

1

2

3

4

5

6

7

5 15 25 35 45 55 More

Freq

uency

Class Frequency

10 but less than 20 3 .15 15

20 but less than 30 6 .30 30

30 but less than 40 5 .25 25

40 but less than 50 4 .20 2050 but less than 60 2 .10 10

Total 20 1.00 100

RelativeFrequency

Percentage

(In a percentage polygon

the vertical axis would

be defined to show the

percentage of

observations per class)


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Organizing Numerical Data:The Cumulative Percentage

Polygon

Ogive: Daily High Temperature

0

20

40

60

80

100

10 20 30 40 50 60Cumulativ

ePercentage

Class LowerBoundary

% Less ThanLower Boundary

10


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Cross Tabulation


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Cross Tabulations:The Contingency Table

A cross-classification (or contingency) tablepresentsthe results of two categorical variables

The categories of one variable are located in the rows,

the categories of the other are located in the columns

The joint responses are classified and shown in the cells

A graphical representation is the side-by-side bar chart


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Cross Tabulations:The Contingency Table

Importance of Brand Name Male Female Total

More 450 300 750

Equal or Less 3300 3450 6750

Total 3750 3750 7500

A survey was conducted to study the importance of brandname to consumers as compared to a few years ago.

The results, classified by gender, were as follows:


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Cross Tabulations:Side-By-Side Bar Charts

Importance of Brand Name

0 500 1000 1500 2000 2500 3000 3500 4000

More

Less or Equal

Response

Number of Responses

Female

Male


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Numerical Data:Scatter Plots

& Time Series PlotsTo create scatter plots & time-series

plots in EXCEL, use the XY(Scatter)

option in the chart wizard.


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Scatter Plots

Scatter plotsare used for numerical data consisting

of paired observations taken from two numerical

variables.

One variable is measured on the vertical axis and the

other variable is measured on the horizontal axis.


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Scatter Plot Example

Volumeper day

Cost perday

23 125

26 140

29 146

33 160

38 167

42 170

50 188

55 195

60 200

Cost per Day vs. Production Volume

0

50

100

150

200

250

20 30 40 50 60 70

Volume per Day

CostperDay


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Time Series Plot

Attendance (in millions) at USA

amusement/theme parks from 2000-2005Year Year

NumberAttendance

2000 0 317

2001 1 319

2002 2 324

2003 3 322

2004 4 328

2005 5 335

A time-series plot is used to study patterns in the

values of a numerical variable over time.

Attendance (in millions) at US Theme Parks

316

320

324

328

332

336

0 1 2 3 4 5 6

Year (Since 2000)

Attendance


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Principles of Excellent Graphs

The graph should not distort the data.

The graph should not contain unnecessary

adornments (chart junk).

The scale on the vertical axis should begin at zero.

The graph should contain a title & properly labeled.

Use the simplest possible graph.


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Graphical Errors: Chart Junk

1960: $1.00

1970: $1.60

1980: $3.10

1990: $3.80

Minimum Wage Minimum Wage

0

2

4

1960 1970 1980 1990

$

Which one is a better presentation?

Example 1


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Graphical Errors:

No Relative Basis

As received by

students.As received by

students.

0

200

300

FR SO JR SR

Freq.

10%

30%

FR SO JR SR

FR = Freshmen, SO = Sophomore, JR = Junior, SR = Senior

100

20%

0%

%

Example 2



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Graphical Errors:

Compressing the Vertical Axis

Quarterly Sales Quarterly Sales

0

25

50

Q1 Q2 Q3 Q4

$

0

100

200

Q1 Q2 Q3 Q4

$

Example 3



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Graphical Errors: No Zero

Point on the Vertical Axis

Hang Seng Index

0

5000

10000

15000

20000

25000

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HSI

Example 4


Hang Seng Index

10000

12000

14000

16000

18000

20000

22000

24000

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HSI

Impact of Financial Tsunami to HSI


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How to Sell a Lie

Point to pictures or graphs

Pictures (relevant or not) often alter our

perceptions of truth Present numbers or tables

Use words like because

Tell a story

ns2 data presenting 14

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