chapter 2 (summarizing data)_student

7/31/2019 Chapter 2 (Summarizing Data)_student

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Chapter 2

Summarizing data

Summarizing Qualitative Data

Summarizing Quantitative Data

Part A


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Why summarizing data?

Survey,investigation

Rawdata

Disadvantage?

How to extract some information from

these data?

- arranging

- putting them intoorder


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I. Summarizing Qualitative Data

Frequency Distribution

Relative Frequency Distribution

Percent Frequency Distribution Bar Graph

Pie Chart


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A frequency distribution is

The objective is

Frequency Distribution


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Example: Marada Inn

Guests staying at Marada Inn wereasked to rate the quality of their

accommodations as being excellent,

above average, average, below average, or

poor. The ratings provided by a sample of 20 guests are:


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Example: Marada Inn

Below Average

Above Average

Above Average

Average

Above Average

Average

Above Average

Average

Above Average

Below Average

Poor

Excellent

Above Average

Average

Above Average

Above Average

Below Average

Poor

Above Average

Average


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Why Use Frequency Distributions?

A frequency distribution is a way tosummarize data

The distribution condenses the raw datainto a more useful form...

and allows for a quick visual interpretationof the data


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The relative frequency of a class is

A relative frequency distribution is



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Ratings Frequency Relative frequency

Poor

Below Average

Average

Above AverageExcellent

Total

2

3

5

91

20


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Bar Graph

A graphical device for depicting qualitative data.

On one axis (usually the horizontal axis), we specifythe label or the name of each of the class.

On the other axis (usually the vertical axis), we specifythe frequency, relative frequency of each class

A bar of fixed width is drawn above each class

label, we extend the height appropriately. The bars are separated to emphasize the fact that each

class is a separate category.


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Insights Gained from the Preceding Pie Chart

Example: Marada Inn


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1. Simple frequency distribution

Simple frequencydistribution consists of alist of data values, eachshowing the number of

items having that value(the frequency).

Data values Frequency

0 10

1 12

2 9

3 8


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Frequency distribution table

Number of childrenin family

Number of workers

0

1

2

3

4

5

6


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2. Grouped frequency distributions

Used when the data set contains a large numberof data values.

A grouped frequency distribution summaries

data into groups of values, each showing thenumber of items having values in the group.

Each group of data value called class

Used for both continuous data and discrete data


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Example: Hudson Auto Repair

The manager of Hudson Auto

would like to have a better

understanding of the cost

of parts used in the engine

tune-ups performed in theshop. She examines 50

customer invoices for tune-ups. The costs of parts,

rounded to the nearest dollar, are listed on the next

slide.


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Example


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Dot Plot

Tune-up Parts Cost


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Hi


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Histogram

Tune-up Parts Cost


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Cumulative Frequency Distribution

Part costs ($) Frequency Cumulativefrequency

Relativecumulativefrequency

Hudson Auto Repair


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Chapter 2

Summarizing data

Exploratory Data Analysis

Crosstabulation and Scatter Diagrams

Part B

x

y

E l t D t A l i


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Exploratory Data Analysis

The techniques of exploratory data analysis consist of

simple arithmetic and easy-to-draw pictures that canbe used to summarize data quickly.

One such technique is the stem-and-leaf display.


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Stem-and-Leaf Display

E l H d A t R i


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The manager of Hudson Auto

would like to have a better

understanding of the cost

of parts used in the engine

tune-ups performed in the

shop. She examines 50

customer invoices for tune-ups. The costs of parts,

rounded to the nearest dollar, are listed on the next

slide.

E l H d A t R i


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Sample of Parts Cost for 50 Tune-ups

91 78 93 57 75 52 99 80 97 62

71 69 72 89 66 75 79 75 72 76

104 74 62 68 97 105 77 65 80 109

85 97 88 68 83 68 71 69 67 74

62 82 98 101 79 105 79 69 62 73


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St etched Stem and Leaf Displa


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Stretched Stem-and-Leaf Display

St d L f Di l


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Stem-and-Leaf Display

Leaf Units

Where the leaf unit is not shown, it is assumedto equal 1.

Leaf units may be 100, 10, 1, 0.1, and so on.

In the preceding example, the leaf unit was 1.

A single digit is used to define each leaf.

Example: Leaf Unit 0 1


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Example: Leaf Unit = 0.1

If we have data with values such as8.6 11.7 9.4 9.1 10.2 11.0 8.8

a stem-and-leaf display of these data will be

Example: Leaf Unit 10


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Example: Leaf Unit = 10

If we have data with values such as

1806 1717 1974 1791 1682 1910 1838

a stem-and-leaf display of these data will be

Crosstabulations and Scatter


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Crosstabulations and ScatterDiagrams

Crosstabulation and a scatter diagram are twomethods for summarizing the data for two (or more)variables simultaneously.

Often a manager is interested in tabular andgraphical methods that will help understand the

relationship between two variables.

So far we have focused on methods that are usedto summarize the data for one variable at a time.

Crosstabulation


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Crosstabulation

Crosstabulation can be used when:

A crosstabulation is


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Cross-tabulation

Example: Finger Lakes Homes

The number of Finger Lakes homes sold for each

style and price for the past two years is shownbelow

Crosstabulation


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Crosstabulation

Insights Gained from Preceding

Crosstabulation

Crosstabulation


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PriceRange Colonial Log Split A-Frame Total

< $99,000

> $99,000

18 6 19 12 55

45

30 20 35 15Total 100

12 14 16 3

Home Style

Crosstabulation

Frequency distributionfor the price variable

Frequency distributionfor the home style variable

Cross-tabulation: Row or Column


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Percentages

Converting the entries in the table into row

percentages or column percentages canprovide additional insight about therelationship between the two variables.

Crosstabulation: Row Percentages


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Crosstabulation: Row Percentages

C t b l ti C l P t


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Crosstabulation: Column Percentages

Scatter Diagram and Trendline


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The general pattern of the plotted points suggests theoverall relationship between the variables.

One variable is shown on the horizontal axis and theother variable is shown on the vertical axis.

A scatter diagram is a graphical presentation of the

relationship between two quantitative variables.

Scatter Diagram and Trendline

A trendline is an approximation of the relationship.

Scatter Diagram


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Scatter Diagram

A Positive Relationship

x

y

Scatter Diagram


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Scatter Diagram

A Negative Relationship

x

y

Scatter Diagram


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Scatter Diagram

No Apparent Relationship

x

y

Example: Panthers Football Team


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Scatter Diagram

The Panthers football team is interestedin investigating the relationship, if any,

between interceptions made and points scored.

1

3

21

3

14

24

1817

30

x= Number ofInterceptions

y= Number ofPoints Scored


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Scatter Diagram



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Insights Gained from the Preceding Scatter Diagram


Tabular and Graphical Procedures


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Tabular and Graphical Procedures

Qualitative Data Quantitative Data

TabularMethods

TabularMethods

GraphicalMethods

GraphicalMethods

FrequencyDistribution

Rel. Freq. Dist.Crosstabulation

Bar GraphPie Chart

FrequencyDistribution

Rel. Freq. Dist.Cum. Freq. Dist.

Cum. Rel. Freq.DistributionStem-and-Leaf

DisplayCrosstabulation

Dot PlotHistogramOgiveScatter

Diagram

Data

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