2 Organizing and Graphing Data

8/9/2019 2 Organizing and Graphing Data

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Probability & StatisticsProbability & StatisticsProbability & StatisticsProbability & Statistics

Organizing & Graphing DataOrganizing & Graphing Data


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Introduction

When data is collected it needs to be organized insome way so that the pattern of the results canbe seen.

For example, below is an unordered list of theheights of the girls in a first year class, measuredin cm.141, 150, 144, 145, 150, 148, 136, 134, 144, 155,147, 151, 154

We could rearrange it from smallest to highest


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Stem-and-Leaf Diagram

A simple way to see distribution details in a dataset

METHOD: Separate the sorted data series

into leading digits (the stem) and

the trailing digits (theleaves)


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Graphing Data

Goals for effective data presentation:

Present data to display essential information

Communicate complex ideas clearly and accurately

Avoid distortion that might convey the wrong

message


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Types of Data

Data

Categorical Numerical

Discrete Continuous

Examples:

Marital Status Are you registered to

vote? Eye Color

(Defined categories or

groups)

Examples:

Number of Children Defects per hour

(Counted items)

Examples:

Weight Voltage

(Measured characteristics)


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GraphicalPresentation of Data

Data in raw form are usually not easyto use for decision making

Some type oforganizationis needed

Table

Graph The type of graph to use depends on

the variable being summarized


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GraphicalPresentation of Data

Techniques reviewed in this chapter:

Categorical

Variables

Numerical

Variables

Frequency distribution Bar chart Pie chart Pareto diagram

Line chart Frequency distribution Histogram and ogive Stem-and-leaf display Scatter plot

(continued)


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The FrequencyDistribution Table

Example: Hospital Patients by Unit

Hospital Unit Number of Patients

Cardiac Care 1,052

Emergency 2,245

Intensive Care 340Maternity 552

Surgery 4,630(Variables are

categorical)

Summarize data by category


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Bar and Pie

Charts Bar charts and Pie charts are

often used for qualitative(category) data

Height of bar or size of pie sliceshows the frequency orpercentage for each category


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Bar Chart Example

Hospital Patients by Un

0

1000

2000

3000

4000

5000

Card

iac

Care

ergen

cy

ntensive

Care

atern

ity

Surgery

Nu

mberof

patientsperyear

Hospital NumberUnit of Patients

Cardiac Care 1,052

Emergency 2,245

Intensive Care 340

Maternity 552

Surgery 4,630


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Hospital Patients by Un

Emergenc

25%

Maternit6%

Surger53%

Cardiac Car

12%

Intensive Car

4%

Pie Chart Example

(Percentages

are rounded to

the nearest

percent)

Hospital Number % ofUnit of Patients Total

Cardiac Care 1,052 11.93

Emergency 2,245 25.46

Intensive Care 340 3.86

Maternity 552 6.26

Surgery 4,630 52.50


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Pareto Diagram

Used to portray categorical data

A bar chart, where categories are shown in

descending order of frequency

A cumulative polygon is often shown in the

same graph

Used to separate the vital few from the

trivial many


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Example: 400 defective items areexamined for cause of defect:

Source of

Manufacturing Error

Number of

defectsBad Weld 34

Poor Alignment 223

Missing Part 25

Paint Flaw 78Electrical Short 19

Cracked case 21

Total 400

Pareto Diagram Example


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Step 1: Sort by defect cause, in descending order

Step 2: Determine % in each category

Source of

Manufacturing

Error

Number of defects % of Total

Defects

Poor Alignment 223 55.75

Paint Flaw 78 19.50

Bad Weld 34 8.50

Missing Part 25 6.25Cracked case 21 5.25

Electrical Short 19 4.75

Total 400 100%


(continued)


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cumulative%

(linegraph)

%

ofde

fectsineach

category

(bargra

ph)

Pareto Diagram: Cause of M anufactur in

0 %

1 0%

2 0%

3 0%

4 0%

5 0%

6 0%

P o o r Alig n m e n t P a in t F la w B ad W e ld M is s in g Pa rt C ra c ke d ca s e E le c tr ic a l S h or t

0 %

1 0%

2 0%

3 0%

4 0%

5 0%

6 0%

7 0%

8 0%

9 0%

100%

Step 3: Show results graphically(continued)


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Graphs for Time-Series

Data A line chart (time-series plot) is used toshow the values of a variable over time

Time is measured on the horizontal axis

The variable of interest is measured onthe vertical axis


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Line Chart ExampleMagazine Subscriptions by Ye

0

50

100

150

200

250

300

350

1

990

1

991

1

992

1

993

1

994

1

995

1

996

1

997

1

998

1

999

2

000

2

001

2

002

2

003

2

004

2

005

2

006

Thousandsofsubscribers


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Frequency Histogram

One of the more commonly usedpictorials in statistics is the

frequency histogram, which in someways similar to a bar chart and tellshow many items are in each numericalcategory.


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Example of Frequency

Histogram


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Example of Frequency

Histogram


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Frequency Polygon

In this chart, the frequency of each class

is indicated by points or dots drawn at themidpoints of each class interval.


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Example of Frequency Polygon


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Cumulative Frequency or Ogive

An ogive (a cumulative line graph) is bestused when you want to display the total atany given time.

The relative slopes from point to point willindicate greater or lesser increases; forexample, a steeper slope means a greater

increase than a more gradual slope.


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Example of Cumulative Frequencyor Ogive

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