Descriptive Statistics: Tabular and Graphical Presentations ■ Summarizing Qualitative Data ■ Summarizing Quantitative Data
Descriptive Statistics:Tabular and Graphical Presentations
� Summarizing Qualitative Data� Summarizing Quantitative Data
Summarizing Qualitative Data
� Frequency Distribution� Relative Frequency Distribution� Cumulative Frequency� Cumulative Relative Frequency � Bar Graph� Pie Chart
Example: Marada Inn
Guests staying at Marada Inn wereasked to rate the quality of their accommodations as being excellent,above average, average, below average, orpoor. The ratings provided by a sample of 20 guests are:
Below AverageAbove AverageAbove AverageAverageAbove Average AverageAbove Average
Average Above AverageBelow AveragePoorExcellent Above AverageAverage
Above AverageAbove AverageBelow AveragePoorAbove Average Average
Frequency Distribution
PoorBelow AverageAverageAbove AverageExcellent
23591
Total 20
Rating FrequencyCumulativeFrequency
25101920 2+3+5 =10
Relative Frequency andPercent Frequency Distributions
PoorBelow AverageAverageAbove AverageExcellent
.10
.15
.25
.45
.05Total 1.00
.10
.25
.50
.951.0
RelativeFrequency
CumulativeRelativeFrequencyRating
.10+.15 =.25
1/20 = .05
PoorPoor BelowAverageBelow
AverageAverageAverage Above
AverageAbove
AverageExcellentExcellent
Freq
uenc
yFr
eque
ncy
RatingRating
Bar Graph
112233445566778899
1010Marada Inn Quality Ratings
BelowAverage
15%
BelowAverage
15%
Average25%
Average25%
AboveAverage
45%
AboveAverage
45%
Poor10%Poor10%
Excellent5%
Excellent5%
Marada Inn Quality Ratings
Pie Chart
Summarizing Quantitative Data
� Frequency Distribution� Relative Frequency Distributions� Histogram� Cumulative Distributions
Example: Hudson Auto Repair
The manager of Hudson Autowould like to have a betterunderstanding of the costof parts used in the enginetune-ups performed in theshop. She examines 50customer invoices for tune-ups. The costs of parts,rounded to the nearest dollar, are listed on the nextslide.
Example: Hudson Auto Repair
� Sample of Parts Cost for 50 Tune-ups
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
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
Frequency Distribution
� Guidelines for Selecting Number of Classes• Use between 5 and 20 classes.• Data sets with a larger number of elements
usually require a larger number of classes.• Smaller data sets usually require fewer classes
Frequency Distribution
� Guidelines for Selecting Width of Classes
Largest Data Value Smallest Data ValueNumber of Classes
− Largest Data Value Smallest Data ValueNumber of Classes
−
•Use classes of equal width.•Approximate Class Width =
Frequency Distribution
For Hudson Auto Repair, if we choose six classes:
50-5960-69 70-7980-8990-99
100-109
21316775
Total 50
Parts Cost ($) Frequency
Approximate Class Width = (109 - 52)/6 = 9.5 ≅ 10
Relative Frequency Distribution
50-5960-69 70-7980-8990-99
100-109
PartsCost ($)
.04
.26
.32
.14
.14
.10Total 1.00
RelativeFrequency
2/50
Cumulative Distributions
� Hudson Auto Repair
50 - 5960 - 69 70 - 7980 - 8990 - 99
100 - 109
Cost ($)CumulativeFrequency
CumulativeRelative
Frequency
CumulativePercent
Frequency2
1531384550
.04
.30
.62
.76
.901.00
430627690
100
2 + 13 15/50 .30(100)
Frequency2
1316775
Histogram
22
44
66
88
1010
1212
1414
1616
1818
PartsCost ($)
PartsCost ($)
Freq
uenc
yFr
eque
ncy
50−59 60−69 70−79 80−89 90−99 100-11050−59 60−69 70−79 80−89 90−99 100-110
Tune-up Parts Cost
� Symmetric• Left tail is the mirror image of the right tail• Examples: heights and weights of people
Histogram
Rela
tive
Freq
uenc
yRe
lativ
e Fr
eque
ncy
.05.05
.10.10
.15.15
.20.20
.25.25
.30.30
.35.35
00
Histogram
� Moderately Skewed Left• A longer tail to the left• Example: exam scores
Rela
tive
Freq
uenc
yRe
lativ
e Fr
eque
ncy
.05.05
.10.10
.15.15
.20.20
.25.25
.30.30
.35.35
00
� Moderately Right Skewed• A Longer tail to the right• Example: housing values
Histogram
Rela
tive
Freq
uenc
yRe
lativ
e Fr
eque
ncy
.05.05
.10.10
.15.15
.20.20
.25.25
.30.30
.35.35
00
Histogram
� Highly Skewed Right• A very long tail to the right• Example: executive salaries
Rela
tive
Freq
uenc
yRe
lativ
e Fr
eque
ncy
.05.05
.10.10
.15.15
.20.20
.25.25
.30.30
.35.35
00
Scatter Diagram
� A Positive Relationship
x
y
Scatter Diagram
� A Negative Relationship
x
y
Scatter Diagram
� No Apparent Relationship
x
y
Example: Panthers Football Team
� Scatter DiagramThe Panthers football team is interested
in investigating the relationship, if any,between interceptions made and points scored.
13213
1424181730
x = Number ofInterceptions
y = Number ofPoints Scored
Scatter Diagram
y
x
Number of Interceptions
Num
ber o
f Poi
nts S
core
d
51015202530
0
35
1 2 30 4
Tabular and Graphical Procedures
Qualitative Data Quantitative Data
TabularMethods
TabularMethods
GraphicalMethods
GraphicalMethods
•FrequencyDistribution
•Rel. Freq. Dist.•Cumulative Freq.
Distribution•Cumulative Rel. Freq.
Distribution
•Bar Graph•Pie Chart •Frequency
Distribution•Rel. Freq. Dist.•Cum. Freq. Dist.•Cum. Rel. Freq.
Distribution
•Histogram•Scatter
Diagram
Data