Descriptive Statistics: Tabular and Graphical Presentations

1 Slide

Descriptive Statistics:Tabular and Graphical Presentations

Chapter 2BA 201 – Spring 2011

2 Slide

Summarizing Data Using Tabular and Graphical Presentations

Categorical Data Frequency, Relative

Frequency, and Percent Frequency Distributions

Bar Chart Pie Chart Cross Tabulations

Quantitative Data Frequency, Relative

Frequency, and Percent Frequency Distributions

Dot Plot Histogram Cumulative

Distributions Ogive Cross Tabulations Stem-and-Leaf Scatter Diagrams

3 Slide

Frequency Distribution

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

4 Slide

Frequency Distribution Categorical Data

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

Marada Inn Ratings – customer ratings

Count ratings in each category

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Frequency DistributionCategorical Data

PoorBelow AverageAverageAbove AverageExcellent

2 3 5 9 1

Total 20

Rating Frequency

Count for class

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Frequency DistributionQuantitative Data

Hudson Auto Repair – cost of parts in tune-up

91 78 93 57 75 52 99 80 97 6271 69 72 89 66 75 79 75 72 76104 74 62 68 97 105 77 65 80 10985 97 88 68 83 68 71 69 67 7462 82 98 101 79 105 79 69 62 73

7 Slide

Frequency DistributionQuantitative Data

1. Determine the number of non-overlapping classes.• 5 to 20 classes based on quantity of data.

2. Determine the width of each class.• Equal width.• =(largest value – smallest value)/# of

classes3. Determine the class limits.

• Each item in one class only.

8 Slide

Frequency Distribution

Using six classes. Largest = 109, Smallest = 52.

50-59

60-69 70-79 80-89 90-99

100-109

2 13 16 7 7 5Total 50

Parts Cost ($) Frequency

Approximate Class Width = (109 - 52)/6 = 9.5 10

Hudson Auto Repair

9 Slide

Relative Frequency Distribution

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

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

10 Slide

Percent Frequency Distribution

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

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

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Relative Frequency andPercent Frequency Distributions

PoorBelow AverageAverageAbove AverageExcellent

.10 .15 .25 .45 .05 1.00

10 15 25 45 5 100

RelativeFrequency

PercentFrequencyRating

.10(100) = 10

1/20 = .05Total

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Bar Chart

A bar chart is a graphical device for depicting qualitative data.• Horizontal axis – labels for classes.• Vertical axis – frequency scale.

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Poor BelowAverage

Average AboveAverage

Excellent

Freq

uenc

y

Rating

Bar Chart

123456789

10 Marada Inn Quality Ratings

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Pareto Diagram

Bar Chart Bars arranged in descending order from left to

right.

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Freq

uenc

y

Rating123456789

10 Marada Inn Quality Ratings

PoorBelowAverage

Average AboveAverage

Excellent

Pareto Diagram

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Pie Chart First draw a circle; then use the relative

frequencies to subdivide the circle into sectors that correspond to the relative frequency for each class.

Since there are 360 degrees in a circle, a class with a relative frequency of .25 would consume .25(360) = 90 degrees of the circle.

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BelowAverage 15%

Average 25%

AboveAverage 45%

Poor10%

Excellent 5%

Marada Inn Quality Ratings

Pie Chart

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Frequency Distribution Practice

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Dot Plot

A horizontal axis shows the range of data values.

Each data value represented by a dot above the axis.

20 Slide

Dot Plot

50 60 70 80 90 100 110Cost ($)

Tune-up Parts CostHudson Auto Repair

21 Slide

Histogram

Variable of interest is on the horizontal axis. A rectangle is drawn above each class interval

with its height corresponding to the interval’s frequency, relative frequency, or percent frequency.

No separation between classes.

22 Slide

Histogram

2468

1012141618

PartsCost ($)

Freq

uenc

y

50-59 60-69 70-79 80-89 90-99 100-110

Tune-up Parts Cost

Hudson Auto Repair

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Skewness

Symmetric

Skewed Left Skewed Right

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Histogram Practice

b. Start the first class at zero.

25 Slide

Cumulative Distributions

Shows items with values less than or equal to upper limit of class:• Frequency – number of items.• Relative frequency – proportion of items.• Percent frequency – percentage of items.

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Cumulative Distributions

Hudson Auto Repair

< 59

< 69 < 79 < 89 < 99

< 109

Cost ($) CumulativeFrequency

CumulativeRelative

Frequency

CumulativePercent

Frequency 2 15 31 38 45

50

.04 .30 .62 .76 .90

1.00

4 30 62 76 90

100

2 + 13 15/50 .30(100

)

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Ogive

An ogive is a graph of a cumulative distribution.

Data values on horizontal axis. Cumulative measure on vertical axis. Frequency of each class plotted as a point. Straight lines connect points.

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PartsCost ($)

20

40

60

80

100

Cum

ulat

ive

Perc

ent F

requ

ency

50 60 70 80 90 100 110

Ogive with Cumulative Percent Frequencies

Tune-up Parts Cost

Hudson Auto Repair

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Stem-and-Leaf Display

Easy way to show shape of rank order and shape of the distribution.

Leaf = right most digit. Stem = left most digit(s).

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Stem-and-Leaf Display

56789

10

2 7 2 2 2 2 5 6 7 8 8 8 9 9 9

1 1 2 2 3 4 4 5 5 5 6 7 8 9 9 9 0 0 2 3 5 8 9 1 3 7 7 7 8 9 1 4 5 5 9

a stema leaf

Hudson Auto Repair

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Example of Leaf Unit = 0.1

If we have data with values such as

8 91011

Leaf Unit = 0.16 81 420 7

8.6 11.7 9.4 9.1 10.2 11.0 8.8a stem-and-leaf display of these data will be

32 Slide

Stretched Stem-and-Leaf Display

5 5 91 47 7 7 8 91 35 8 90 0 2 35 5 5 6 7 8 9 9 91 1 2 2 3 4 45 6 7 8 8 8 9 9 92 2 2 2725

566778899

1010

Hudson Auto Repair

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Stem and Leaf Practice

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Crosstabulation

A crosstabulation is a tabular summary for two variables.

Left and top margins define classes for variables.

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PriceRange Colonial Log Split A-FrameTotal

< $200,000> $200,000

18 6 19 12 5545

30 20 35 15Total 10012 14 16 3

Home Style

Crosstabulation

Finger Lakes HomesThe number of Finger Lakes homes sold for each style and price for the past two years is shown below.

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PriceRange Colonial Log Split A-FrameTotal

< $200,000> $200,000

18 6 19 12 5545

30 20 35 15Total 10012 14 16 3

Home Style

CrosstabulationFrequencydistribution

for theprice range

variable

Frequency distribution for

the home style variable

Finger Lakes Homes

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PriceRange Colonial Log Split A-FrameTotal

< $200,000> $200,000

32.73 10.91 34.55 21.82100100

Note: row totals are actually 100.01 due to rounding.26.67 31.11 35.56 6.67

Home Style

(Colonial and > $200K)/(All > $200K) x 100 = (12/45) x 100

Crosstabulation: Row Percentages

Finger Lakes Homes

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PriceRange Colonial Log Split A-Frame

< $200,000> $200,000

60.00 30.00 54.29 80.0040.00 70.00 45.71 20.00

Home Style

100 100 100 100Total

(Colonial and > $200K)/(All Colonial) x 100 = (12/30) x 100

Crosstabulation: Column Percentages

Finger Lakes Homes

39 Slide

Cross Tabulation Practice

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Scatter Diagram and Trendline

A scatter diagram is a graphical presentation of the relationship between two quantitative variables.

A trendline provides an approximation of the relationship.

41 Slide

Panthers Football Team

13213

1424181730

Number ofInterceptions

Number of Points Scored

Scatter Diagram

The Panthers football team is interested in investigating the relationship, if any, between interceptions made and points scored.

42 Slide

Scatter Diagram

Number of Interceptions

Num

ber o

f Poi

nts S

core

d

51015202530

0

35

1 2 30 4

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