1 1 Slide © 2005 Thomson/South-Western Introduction to Statistics Chapter 2 Descriptive Statistics

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© 2005 Thomson/South-Western© 2005 Thomson/South-Western

Introduction to StatisticsIntroduction to Statistics

Chapter 2

Descriptive Statistics

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Slides Prepared bySlides Prepared by

JOHN S. LOUCKSJOHN S. LOUCKSSt. Edward’s UniversitySt. Edward’s University

Slides Prepared bySlides Prepared by

JOHN S. LOUCKSJOHN S. LOUCKSSt. Edward’s UniversitySt. Edward’s University

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Chapter 2Chapter 2Descriptive Statistics:Descriptive Statistics:

Tabular and Graphical PresentationsTabular and Graphical PresentationsPart APart A

Summarizing Qualitative DataSummarizing Qualitative Data Summarizing Quantitative DataSummarizing Quantitative Data

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Summarizing Qualitative DataSummarizing Qualitative Data

Frequency DistributionFrequency Distribution Relative Frequency Distribution Relative Frequency Distribution Percent Frequency DistributionPercent Frequency Distribution Bar GraphBar Graph Pie ChartPie Chart

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A A frequency distributionfrequency distribution is a tabular summary of is a tabular summary of data showing the frequency (or number) of itemsdata showing the frequency (or number) of items in each of several non-overlapping classes.in each of several non-overlapping classes.

A A frequency distributionfrequency distribution is a tabular summary of is a tabular summary of data showing the frequency (or number) of itemsdata showing the frequency (or number) of items in each of several non-overlapping classes.in each of several non-overlapping classes.

The objective is to The objective is to provide insightsprovide insights about the data about the data that cannot be quickly obtained by looking only atthat cannot be quickly obtained by looking only at the original data.the original data.

The objective is to The objective is to provide insightsprovide insights about the data about the data that cannot be quickly obtained by looking only atthat cannot be quickly obtained by looking only at the original data.the original data.

Frequency DistributionFrequency Distribution

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Example: Marada InnExample: Marada Inn

Guests staying at Marada Inn wereGuests staying at Marada Inn wereasked to rate the quality of their asked to rate the quality of their accommodations as being accommodations as being excellentexcellent,,above averageabove average, , averageaverage, , below averagebelow average, or, orpoorpoor. The ratings provided by a sample of 20 . The ratings provided by a sample of 20

guests are:guests are:

Below AverageBelow Average

Above AverageAbove Average


AverageAverage

Above Average Above Average

AverageAverage


Average Average



PoorPoor

Excellent Excellent


AverageAverage




PoorPoor

Above Average Above Average

AverageAverage

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Frequency DistributionFrequency Distribution

PoorPoorBelow AverageBelow AverageAverageAverageAbove AverageAbove AverageExcellentExcellent

22 33 55 99 11

TotalTotal 20 20

RatingRating FrequencyFrequency

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The The relative frequencyrelative frequency of a class is the fraction of a class is the fraction or proportion of the total number of data itemsor proportion of the total number of data items belonging to the class.belonging to the class.

The The relative frequencyrelative frequency of a class is the fraction of a class is the fraction or proportion of the total number of data itemsor proportion of the total number of data items belonging to the class.belonging to the class.

A A relative frequency distributionrelative frequency distribution is a tabular is a tabular summary of a set of data showing the relativesummary of a set of data showing the relative frequency for each class.frequency for each class.

A A relative frequency distributionrelative frequency distribution is a tabular is a tabular summary of a set of data showing the relativesummary of a set of data showing the relative frequency for each class.frequency for each class.

Relative Frequency DistributionRelative Frequency Distribution

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Percent Frequency DistributionPercent Frequency Distribution

The The percent frequencypercent frequency of a class is the relative of a class is the relative frequency multiplied by 100.frequency multiplied by 100. The The percent frequencypercent frequency of a class is the relative of a class is the relative frequency multiplied by 100.frequency multiplied by 100.

AA percent frequency distributionpercent frequency distribution is a tabular is a tabular summary of a set of data showing the percentsummary of a set of data showing the percent frequency for each class.frequency for each class.

AA percent frequency distributionpercent frequency distribution is a tabular is a tabular summary of a set of data showing the percentsummary of a set of data showing the percent frequency for each class.frequency for each class.

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Relative Frequency andRelative Frequency andPercent Frequency DistributionsPercent Frequency Distributions

PoorPoor


AverageAverage


ExcellentExcellent

.10.10

.15.15

.25.25

.45.45

.05.05

TotalTotal 1.00 1.00

1010

1515

2525

4545

55

100100

RelativeRelativeFrequencyFrequency

PercentPercentFrequencyFrequencyRatingRating

.10(100) = .10(100) = 1010

1/20 1/20 = .05= .05

FrequencyFrequency 22

33

55

99

11

2020

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Bar GraphBar Graph

A A bar graphbar graph is a graphical device for depicting is a graphical device for depicting qualitative data.qualitative data. On one axis (usually the horizontal axis), we specifyOn one axis (usually the horizontal axis), we specify the labels that are used for each of the classes.the labels that are used for each of the classes. A A frequencyfrequency, , relative frequencyrelative frequency, or , or percent frequencypercent frequency scale can be used for the other axis (usually thescale can be used for the other axis (usually the vertical axis).vertical axis). Using a Using a bar of fixed widthbar of fixed width drawn above each class drawn above each class label, we extend the height appropriately.label, we extend the height appropriately.

The The bars are separatedbars are separated to emphasize the fact that each to emphasize the fact that each class is a separate category.class is a separate category.

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PoorPoor BelowAverageBelow

AverageAverageAverage Above

Average Above

AverageExcellentExcellent

Fre

qu

en

cy

Fre

qu

en

cy

RatingRating

Bar GraphBar Graph

1122

33

44

55

66

77

88

991010

Marada Inn Quality RatingsMarada Inn Quality Ratings

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Pie ChartPie Chart

The The pie chartpie chart is a commonly used graphical device is a commonly used graphical device for presenting relative frequency distributions forfor presenting relative frequency distributions for qualitative data.qualitative data. First draw a First draw a circlecircle; then use the relative; then use the relative frequencies to subdivide the circlefrequencies to subdivide the circle into sectors that correspond to theinto sectors that correspond to the

relative frequency for each class.relative frequency for each class. Since there are 360 degrees in a circle, Since there are 360 degrees in a circle,

a class with a relative frequency of .25 woulda class with a relative frequency of .25 would

consume .25(360) = 90 degrees of the circle.consume .25(360) = 90 degrees of the circle.

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BelowAverage 15%

BelowAverage 15%

Average 25%Average 25%

AboveAverage 45%

AboveAverage 45%

Poor10%Poor10%

Excellent 5%Excellent 5%

Marada InnMarada Inn Quality Quality RatingsRatings

Marada InnMarada Inn Quality Quality RatingsRatings

Pie ChartPie Chart

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Insights Gained from the Preceding Pie Insights Gained from the Preceding Pie ChartChart

Example: Marada InnExample: Marada Inn

• One-half of the customers surveyed gave MaradaOne-half of the customers surveyed gave Marada a quality rating of “above average” or “excellent”a quality rating of “above average” or “excellent” (looking at the left side of the pie). This might(looking at the left side of the pie). This might please the manager.please the manager.

• For For eacheach customer who gave an “excellent” rating, customer who gave an “excellent” rating, there were there were twotwo customers who gave a “poor” customers who gave a “poor” rating (looking at the top of the pie). This shouldrating (looking at the top of the pie). This should displease the manager.displease the manager.

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In Class Group ExerciseIn Class Group Exercise

NameName FrequencyFrequency

BrownBrown 77

DavisDavis 66

JohnsonJohnson 1010

JonesJones 77

SmithSmith 1212

WilliamsWilliams 88

5050

The Following are the The Following are the voices gained by each voices gained by each representative of one representative of one class in a school class in a school

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5 a5 a

NameName FrequencyFrequencyRelative Relative

FrequencyFrequencyPercent Percent

FrequencyFrequency

BrownBrown 77 .14.14 14%14%

DavisDavis 66 .12.12 12%12%

JohnsonJohnson 1010 .20.20 20%20%

JonesJones 77 .14.14 14%14%

SmithSmith 1212 .24.24 24%24%

WilliamsWilliams 88 .16.16 16%16%

5050 1.001.00 100%100%

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5 b5 b

0

2

4

6

8

10

12

14

Brown Davis Johnson Jones Smith Williams

Frequency

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5c5c

% Degrees

Brown 0.14 50.4

Davis 0.12 43.2

Johnson 0.20 72

Jones 0.14 50.4

Smith 0.24 86.4

Williams 0.16 57.6

1.00 360

Percentage

14%

12%

20%14%

24%

16%Brown

Davis

Johnson

Jones

Smith

Williams

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5 d5 d

Most common: Smith, Johnson and Williams Most common: Smith, Johnson and Williams

Documents

1 1 Slide © 2005 Thomson/South-Western Introduction to Statistics Chapter 2 Descriptive Statistics