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Module 1
Application of Quantitative Methods in ManagerialDecision Making Data Processing - Classification Summarization Tabulation of data Presentation (Tabular & Graphic) Frequency Distribution
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Summarizing data using diagrams
Cross-sectional data are collected at the sameor approximately the same point in time.
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Flowofwater(cfs,cubicfootpersecond)
Flow of water in Colorado River, USA
Time series graph
Time series data are collected over several time periods.
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Which graph to use depends on
type of data what you want to illustrate available statistical software
1. Line diagram2. Pie chart3. Bar chart4. Scatter plot
BrandCol Palm
Unitssold 90
Lakme 120
P & G 80
Revlon 60
Yardley 100
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020406080
100120140
C o l_ P
a l m L a
k m e
P & G
R e v l o
n
Y a r d l
e y
Brand
U n
i t s a
l e s
Series1
Line Diagram
Used for categoricaldata
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C o l_P a l
La km e
P & G
R e vlon
Yard ley
Pie chart
Used for categoricaldata
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020406080
100120140
C o l_ P
a l m L a k
m e P & G
R e v l o
n
Y a r d l e
y
Bran
U n i t s a l e s
Ser ies1
Bar chart
Used for categoricaldata
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Composite bar chart
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Brand UnitSales
Duration of display
No. of insertions per day on TV
Col_Palm 40 6 10Dabur 90 3 12Garnier 20 1 6
Himalaya 60 4 9Lakme 110 6 15Mabellene 40 2 3P & G 80 1 12Revlon 60 5 4Yardley 100 2 5
Total:
600
30 days
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0
20
40
60
80
10 0
12 0
0 2 4 6 8
Display-duration (in days)
U n
i t s a
l e s
Series1
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020406080
100120
0 10 20 30TV insertions per day
U n
i t s a
l e
Series1
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0
20
40
60
80
100
120
0 2 4 6 8
Display-duration (in da ys)
U n
i t s a
l e s
Series1
0204060
80100120
0 10 20 30
TV insertions per day
U n
i t s a
l e
Series1
01
2
3
4
5
67
0 10 20 30
TV insertions per day
D i s
p l a y - d u r a
t i o n
Series1
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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 invoicesfor tune-ups. The costs of parts,rounded off to the nearest dollar,
are listed on the next slide.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
Example 1
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Frequency Distributionof engine tune-ups
50-59
60-69
70-79
80-89
90-99
00-109
2
13
167
7
550
Cost ($) Frequency0.04
0.26
0.320.14
0.14
0.101.00
Relative Frequency
2 + 13
Cumulative Frequency
less than more than2
15
3138
45
50
50
48
3518
12
5
5 + 7
45 tune-upscost lessthan $ 100
12 tune-upscost morethan $ 99
2/50 =
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Tune-upCost ($)Tune-upCost ($)
1010
2020
3030
4040
5050
Frequenc
y
Frequency
60 70 80 90 100 11060 70 80 90 100 110
Ogiveless than ogive
median
more than ogive
?
How many invoiceswill have the costexceeding $ 95?
How many invoices will have the costlying in the range $ 65 to $ 75?
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Histogram
Unlike a bar graph, a histogram has no natural
separation between rectangles of adjacent classes.
22446688
10101212141416161818
Cost ($)Cost ($)
F
requency
F
requency
50-59 60-69 70-79 80-89 90-99 100-11050-59 60-69 70-79 80-89 90-99 100-110
Bar chart is for categorical data
Histogram is for numerical data
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18 23 28
0
10
20
30
40
50
60
Age (in years)
F r e q u e n c y
( C o u n
t )
Age of Spring 1998 Stat 250 Students
students
Too few categories
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2 3 4
0
1
2
3
4
5
6
7
GPA
F r e q u e n c y
( C o u n
t )
GPAs of Spring 1998 Stat 250 Students
92 students
Too many categories
G t t i t M d I k d t t th lit f
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Guests staying at Marada Inn were asked to rate the quality of their accommodations as being excellent, above average,average, below average, or poor .The ratings provided by a sampleof 20 guests are:
Below Average
Above AverageAbove Average
Average
Above Average
AverageAbove Average
Average
Above Average
Below Average
Poor ExcellentAbove AverageAverage
Above AverageAbove AverageBelow AveragePoor Above AverageAverage
Frequency Distribution
Poor Below AverageAverageAbove AverageExcellent
23591
Total 20
Rating Frequency
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Leaf Unit = 0.1
8
91011
6 8
1 420 7
8.6 11.7 9.4 9.1 10.2 11.0 8.8
Leaf Unit = 10 1806 1717 1974 1791 1682 1910 1838
16171819
81 90 31 7
The 82 in 1682is rounded downto 80 and isrepresented as an 8
A single digit is used to define each leaf
Leaf units may be 100, 10, 1, 0.1, and so on
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stem and leaf plot frequency distribution
Displays the original data Is a numerical and pictorialdisplay
Original data is notdisplayed Is only a pictorial display
