PERTEMUAN-01-02 mengenai probabilitas statistika ekonomi dan umum.ppt

Define Statistics
Describe the Uses of Statistics
Distinguish Descriptive & Inferential Statistics
Define Population, Sample, Parameter, and�Statistic
Define Quantitative and Qualitative Data
Define Random Sample

1. Statistics for Business and
Economics
Chapter 1
Statistics, Data, &
Statistical Thinking

2. Learning Objectives
1.Define Statistics
2.Describe the Uses of Statistics
3.Distinguish Descriptive & Inferential Statistics
4.Define Population, Sample, Parameter, and
Statistic
5.Define Quantitative and Qualitative Data
6.Define Random Sample

3. What Is Statistics?
Why?1.Collecting Data
e.g., Survey
2.Presenting Data
e.g., Charts & Tables
3.Characterizing Data
e.g., Average
Data
Analysis
Decision-
Making
© 1984-1994 T/Maker Co.
© 1984-1994 T/Maker Co.

4. Application Areas
•Economics
–Forecasting
–Demographics
•Sports
–Individual & Team
Performance
•Engineering
–Construction
–Materials
•Business
–Consumer Preferences
–Financial Trends

5. Statistical Methods
Statistical
Methods
Descriptive
Statistics
Inferential
Statistics

6. Descriptive Statistics
1.Involves
•Collecting Data
•Presenting Data
•Characterizing Data
2.Purpose
•Describe Data
X = 30.5 S
2
= 113
0
25
50
Q1Q2Q3Q4
$

7. 1.Involves
•Estimation
•Hypothesis
Testing
2.Purpose
•Make decisions about
population characteristics
Inferential Statistics
Population?

8. Key Terms
1.Population (Universe)
• All items of interest
2.Sample
• Portion of population
3.Parameter
• Summary measure about population
4.Statistic
• Summary measure about sample
•PP in PPopulation
& PParameter
•SS in SSample
& SStatistic

9. Types of Data
Types of
Data
Quantitative
Data
Qualitative
Data

10. Quantitative Data
Measured on a numeric
scale.
• Number of defective
items in a lot.
• Salaries of CEO's of
oil companies.
• Ages of employees at
a company.
3
52
71
4
8
943
120
12
21

11. Qualitative Data
Classified into categories.
• College major of each
student in a class.
• Gender of each employee
at a company.
• Method of payment
(cash, check, credit card).
$$ Credit

12. Random Sample
Every sample of size n has an equal chance of
selection.

13. Statistical
Computer Packages
1.Typical Software
•LISREL
• SPSS+AMOS
•SAS
•MINITAB
•STATA
2.Need Statistical
Understanding
•Assumptions
•Limitations

14. Conclusion
1.Defined Statistics
2.Described the Uses of Statistics
3.Distinguished Descriptive & Inferential
Statistics
4.Defined Population, Sample, Parameter,
and Statistic
5.Defined Quantitative and Qualitative Data
6.Defined Random Sample

15. Probability & Statistics
Methods for Describing
Sets of Data

16. Learning Objectives
1.Describe Qualitative Data Graphically
2.Describe Quantitative Data Graphically
3.Explain Numerical Data Properties
4.Describe Summary Measures
5.Analyze Numerical Data Using
Summary Measures

17. Thinking Challenge
Our market share far
exceeds all
competitors! - VP
30%30%
32%32%
34%34%
36%36%
UsYYXX

18. Data Presentation
Data
Presentation
Qualitative
Data
Quantitative
Data
Summary
Table
Stem-&-Leaf
Display
Frequency
Distribution
Histogram
Bar
Graph
Pie
Chart
Pareto
Diagram

19. Presenting
Qualitative Data

20. Data Presentation
Pie
Chart
Pareto
Diagram
Data
Presentation
Qualitative
Data
Quantitative
Data
Summary
Table
Stem-&-Leaf
Display
Frequency
Distribution
Histogram
Bar
Graph

21. Summary Table
1.Lists categories & number of elements in category
2.Obtained by tallying responses in category
3.May show frequencies (counts), % or both
Row Is
Category
Tally:
|||| ||||
|||| ||||
Major Count
Accounting 130
Economics 20
Management 50
Total 200

22. Data Presentation
Pie
Chart
Summary
Table
Data
Presentation
Qualitative
Data
Quantitative
Data
Stem-&-Leaf
Display
Frequency
Distribution
Histogram
Bar
Graph
Pareto
Diagram

23. 0
50
100
150
Acct. Econ. Mgmt.
Major
Bar Graph
Vertical Bars
for Qualitative
Variables
Bar Height
Shows
Frequency or %
Zero Point
Percent
Used
Also
Equal Bar
Widths
F
r
e
q
u
e
n
c
y

24. Data Presentation
Data
Presentation
Qualitative
Data
Quantitative
Data
Summary
Table
Stem-&-Leaf
Display
Frequency
Distribution
Histogram
Bar
Graph
Pie
Chart
Pareto
Diagram

25. Econ.
10%
Mgmt.
25%
Acct.
65%
Pie Chart
1.Shows breakdown of
total quantity into
categories
2.Useful for showing
relative differences
3.Angle size
•(360°)(percent)
Majors
(360°) (10%) = 36°
36°

26. Data Presentation
Data
Presentation
Qualitative
Data
Quantitative
Data
Summary
Table
Stem-&-Leaf
Display
Frequency
Distribution
Histogram
Bar
Graph
Pie
Chart
Pareto
Diagram

27. Pareto Diagram
Like a bar graph, but with the categories arranged by
height in descending order from left to right.
0
50
100
150
Acct. Mgmt. Econ.
Major
Vertical Bars
for Qualitative
Variables
Bar Height
Shows
Frequency or %
Zero Point
Percent
Used
Also
Equal Bar
Widths
F
r
e
q
u
e
n
c
y

28. Thinking Challenge
You’re an analyst for IRI. You want to show the
market shares held by Web browsers in 2006.
Construct a bar graph, pie chart, & Pareto diagram
to describe the data.
Browser Mkt. Share (%)
Firefox 14
Internet Explorer 81
Safari 4
Others 1

29. 0%
20%
40%
60%
80%
100%
FirefoxInternet
Explorer
Safari Others
Bar Graph Solution*
M
a
r
k
e
t

S
h
a
r
e

(
%
)
Browser

30. Pie Chart Solution*
Market Share
Safari; 4%
Firefox;
14%
Internet
Explorer;
81%
Others;
1%

31. Pareto Diagram Solution*
0%
20%
40%
60%
80%
100%
Internet
Explorer
Firefox Safari Others
M
a
r
k
e
t

S
h
a
r
e

(
%
)
Browser

32. Presenting
Quantitative Data

33. Data Presentation
Data
Presentation
Qualitative
Data
Quantitative
Data
Summary
Table
Stem-&-Leaf
Display
Frequency
Distribution
Histogram
Bar
Graph
Pie
Chart
Pareto
Diagram

34. Stem-and-Leaf Display
1. Divide each observation
into stem value and leaf
value
• Stem value defines
class
• Leaf value defines
frequency (count)
2. Data: 21, 24, 24, 26, 27, 27, 30, 32, 38, 41
26
2144677
3028
41

35. Data Presentation
Data
Presentation
Qualitative
Data
Quantitative
Data
Summary
Table
Stem-&-Leaf
Display
Frequency
Distribution
Histogram
Bar
Graph
Pie
Chart
Pareto
Diagram

36. Frequency Distribution
Table Steps
1.Determine range
2.Select number of classes
• Usually between 5 & 15 inclusive
3.Compute class intervals (width)
4.Determine class boundaries (limits)
5.Compute class midpoints
6.Count observations & assign to classes

37. INCOME
•4300, 3120, 5530, 4000, 2010, 1600,
3190, 8230, 1020, 4280, 3490, 4390,
3490, 3950, 1390, 8990, 1270, 9560,
5240, 4580

38. 1. Determine the range
Range (R) = highest value – lowest value
2. Number of classes
C=1 + 10/3 x log N ( N = number of observation)
3. Class Interval
CI = R/C (rounded)
3a. Upper class limit – lower class limit
b. Lower Class Bounddary, upper class boundary
4. Class Boundaries
Lowest Boundaries value <= lowest value
Highest Boundaries value >= Highest Value
New Lowest Boundaries – x ( any value)
New Highest Boundaries + x ( any Value)
5. New CI will be rounded/integer value
6. Class Mid Point
CM = (Lower + Upper Boundaries) / 2

39. 0
1
2
3
4
5
Histogram
Frequency
Relative
Frequency
Percent
015.525.535.545.555.5
Lower Boundary
Bars
Touch
Class Freq.
15.5 – 25.5 3
25.5 – 35.5 5
35.5 – 45.5 2
Count

40. Frequency Distribution Table
Example
Raw Data: 24, 26, 24, 21, 27 27 30, 41, 32, 38
Boundaries
(Lower + Upper Boundaries) / 2
Width
Class MidpointFrequency
15.5 – 25.5 20.5 3
25.5 – 35.5 30.5 5
35.5 – 45.5 40.5 2

41. Relative Frequency &
% Distribution Tables
Percentage
Distribution
Relative Frequency
Distribution
Class Prop.
15.5 – 25.5.3
25.5 – 35.5.5
35.5 – 45.5.2
Class %
15.5 – 25.530.0
25.5 – 35.550.0
35.5 – 45.520.0

42. Data Presentation
Data
Presentation
Qualitative
Data
Quantitative
Data
Summary
Table
Stem-&-Leaf
Display
Frequency
Distribution
Histogram
Bar
Graph
Pie
Chart
Pareto
Diagram

43. Numerical Data Properties

44. Thinking Challenge
... employees cite low pay --
most workers earn only
$20,000.
... President claims average
pay is $70,000!
$400,000$400,000
$70,000$70,000
$50,000$50,000
$30,000$30,000
$20,000$20,000

45. Standard Notation
Measure Sample Population
Mean X 
Standard
Deviation
S 
Variance S
2

2
Size n N

46. Numerical Data Properties
Central Tendency
(Location)
Variation
(Dispersion)
Shape

47. Numerical Data
Properties & Measures
Numerical Data
Properties
Mean
Median
Mode
Central
Tendency
Range
Variance
Standard Deviation
Variation
Percentiles
Relative
Standing
Interquartile Range
Z–scores

48. Central Tendency

49. Numerical Data
Properties & Measures
MeanMean
Median
Mode
Range
Variance
Standard Deviation
Interquartile Range
Numerical Data
Properties
Central
Tendency
Variation
Percentiles
Relative
Standing
Z–scores

50. Mean
1.Measure of central tendency
2.Most common measure
3.Acts as ‘balance point’
4.Affected by extreme values (‘outliers’)
5.Formula (sample mean)
X
X
n
X X X
n
i
i
n
n
 
  


1 1 2
…

51. Mean Example
Raw Data:10.34.98.911.76.37.7
X
X
n
X X X X X X
i
i
n
 
    

    



1 1 2 3 4 5 6
6
10349891176377
6
830
. . . . . .
.

52. Numerical Data
Properties & Measures
Mean
MedianMedian
Mode
Range
Variance
Standard Deviation
Interquartile Range
Numerical Data
Properties
Central
Tendency
Variation
Percentiles
Relative
Standing
Z–scores

53. Median
1.Measure of central tendency
2.Middle value in ordered sequence
• If n is odd, middle value of sequence
• If n is even, average of 2 middle values
3.Position of median in sequence
4.Not affected by extreme values
Positioning Point
n1
2

54. Median Example
Odd-Sized Sample
•Raw Data:24.122.621.523.722.6
•Ordered:21.522.622.623.724.1
•Position:1 2 3 45
Positioning Point
Median






n1
2
51
2
30
226
.
.

55. Median Example
Even-Sized Sample
•Raw Data:10.34.98.911.76.37.7
•Ordered:4.96.37.78.910.311.7
•Position:123456
Positioning Point
Median








n1
2
61
2
35
7789
2
830
.
. .
.

56. Numerical Data
Properties & Measures
Mean
Median
ModeMode
Range
Variance
Standard Deviation
Interquartile Range
Numerical Data
Properties
Central
Tendency
Variation
Percentiles
Relative
Standing
Z–scores

57. Mode
1.Measure of central tendency
2.Value that occurs most often
3.Not affected by extreme values
4.May be no mode or several modes
5.May be used for quantitative or qualitative
data

58. Mode Example
•No Mode
Raw Data:10.34.98.911.76.37.7
•One Mode
Raw Data:6.34.98.9 6.3 4.94.9
•More Than 1 Mode
Raw Data:212828414343

59. Thinking Challenge
You’re a financial analyst
for Prudential-Bache
Securities. You have
collected the following
closing stock prices of new
stock issues: 17, 16, 21, 18,
13, 16, 12, 11.
Describe the stock prices
in terms of central
tendency.

60. Central Tendency Solution*
Mean
X
X
n
X X X
i
i
n
 
  

      



1 1 2 8
8
1716211813161211
8
155
…
.

61. Central Tendency Solution*
Median
•Raw Data:1716211813161211
•Ordered:1112131616171821
•Position:12345678
Positioning Point
Median








n1
2
81
2
45
1616
22
16
.

62. Central Tendency Solution*
Mode
Raw Data: 1716211813161211
Mode = 16

63. Summary of
Central Tendency Measures
Measure Formula Description
Mean Xi / n Balance Point
Median (n+1)
Position
2
Middle Value
When Ordered
Mode none Most Frequent

64. Shape

65. Shape
1.Describes how data are distributed
2.Measures of Shape
• Skew = Symmetry
Right-SkewedLeft-Skewed Symmetric
MeanMean = = MedianMedian MeanMean MedianMedian MedianMedian MeanMean

66. Variation

67. Numerical Data
Properties & Measures
Mean
Median
Mode
RangeRange
Variance
Standard Deviation
Interquartile Range
Numerical Data
Properties
Central
Tendency
Variation
Percentiles
Relative
Standing
Z–scores

68. Range
1.Measure of dispersion
2.Difference between largest & smallest
observations
Range = X
largest – X
smallest
3.Ignores how data are distributed
7788991010 7788991010
Range = 10 – 7 = 3Range = 10 – 7 = 3

69. Numerical Data
Properties & Measures
Mean
Median
Mode
Range
Interquartile Range
VarianceVariance
Standard DeviationStandard Deviation
Numerical Data
Properties
Central
Tendency
Variation
Percentiles
Relative
Standing
Z–scores

70. Variance &
Standard Deviation
1.Measures of dispersion
2.Most common measures
3.Consider how data are distributed
46 1012
X = 8.3
4. Show variation about mean (X or μ)
8

71. Sample Variance Formula
n - 1 in denominator!
(Use N if Population
Variance)
S
X X
n
i
i
n
2
2
1
1




()
X X X X X X
n
n1
2
2
2 2
1

     

()()()
…
=

72. Sample Standard Deviation
Formula
SS
XX
n
XX XX XX
n
i
i
n
n





    



2
2
1
1
2
2
2 2
1
1
()
()()()…

73. Variance Example
Raw Data:10.34.98.911.76.37.7
S
X X
n
X
X
n
S
i
i
n
i
i
n
2
2
1 1
2
2 2 2
1
83
10383 4983 7783
61
6368



 

     


 
 ()
()()()
where .
. . . . . .
.
…

74. Thinking Challenge
•You’re a financial analyst
for Prudential-Bache
Securities. You have
collected the following
closing stock prices of
new stock issues: 17, 16,
21, 18, 13, 16, 12, 11.
•What are the variance
and standard deviation
of the stock prices?

75. Variation Solution*
Sample Variance
Raw Data: 1716211813161211
S
XX
n
X
X
n
S
i
i
n
i
i
n
2
2
1 1
2
2 2 2
1
155
17155 16155 11155
81
1114



 

   


 
 ()
()()()
where .
. . .
.
…

76. Variation Solution*
Sample Standard Deviation
SS
XX
n
i
i
n
 


 


2
2
1
1
1114334
()
. .

77. Summary of
Variation Measures
Measure Formula Description
Range Xlargest – XsmallestTotal Spread
Standard Deviation
(Sample)
XX
n
i


 
2
1
Dispersion about
Sample Mean
Standard Deviation
(Population)
X
N
i X
 

2Dispersion about
Population Mean
Variance
(Sample)
(Xi X)
2
n – 1
Squared Dispersion
about Sample Mean

78. Interpreting Standard
Deviation

79. Interpreting Standard Deviation:
Chebyshev’s Theorem
•Applies to any shape data set
No useful information about the fraction of data in the
interval x – s to x + s
At least 3/4 of the data lies in the interval
x – 2s to x + 2s
At least 8/9 of the data lies in the interval
x – 3s to x + 3s
In general, for k > 1, at least 1 – 1/k
2
of the data lies in
the interval x – ks to x + ks

80. Interpreting Standard Deviation:
Chebyshev’s Theorem
sx3 sx3sx2 sx2sxxsx
No useful information
At least 3/4 of the data
At least 8/9 of the data

81. Chebyshev’s Theorem Example
•Previously we found the mean
closing stock price of new stock
issues is 15.5 and the standard
deviation is 3.34.
•Use this information to form an
interval that will contain at least
75% of the closing stock prices of
new stock issues.

82. Chebyshev’s Theorem Example
At least 75% of the closing stock prices of new stock issues will lie within 2 standard deviations of the mean.
x = 15.5 s = 3.34
(x – 2s, x + 2s) = (15.5 – 2∙3.34, 15.5 + 2∙3.34)
= (8.82, 22.18)

83. Interpreting Standard Deviation:
Empirical Rule
•Applies to data sets that are mound shaped and symmetric
•Approximately 68% of the measurements lie in the
interval μ – σ to μ + σ
•Approximately 95% of the measurements lie in the
interval μ – 2σ to μ + 2σ
•Approximately 99.7% of the measurements lie in the
interval μ – 3σ to μ + 3σ

84. Interpreting Standard Deviation:
Empirical Rule
μ – 3σ μ – 2σ μ – σ μ μ + σ μ +2σ μ + 3σ
Approximately 68% of the measurements
Approximately 95% of the measurements
Approximately 99.7% of the measurements

85. Empirical Rule Example
Previously we found the mean
closing stock price of new
stock issues is 15.5 and the
standard deviation is 3.34. If
we can assume the data is
symmetric and mound shaped,
calculate the percentage of the
data that lie within the intervals
x + s, x + 2s, x + 3s.

86. Empirical Rule Example
Approximately 95% of the data will lie in the interval (x
– 2s, x + 2s),
(15.5 – 2∙3.34, 15.5 + 2∙3.34) = (8.82, 22.18)
Approximately 99.7% of the data will lie in the interval
(x – 3s, x + 3s),
(15.5 – 3∙3.34, 15.5 + 3∙3.34) = (5.48, 25.52)
According to the Empirical Rule, approximately 68% of
the data will lie in the interval (x – s, x + s),
(15.5 – 3.34, 15.5 + 3.34) = (12.16, 18.84)

87. Numerical Measures of
Relative Standing

88. Numerical Data
Properties & Measures
Mean
Median
Mode
Range
Variance
Standard Deviation
Interquartile Range
Numerical Data
Properties
Central
Tendency
Variation
PercentilesPercentiles
Relative
Standing
Z–scores

89. Numerical Measures of
Relative Standing: Percentiles
•Describes the relative location of a
measurement compared to the rest of the data
•The p
th
percentile is a number such that p% of
the data falls below it and (100 – p)% falls
above it
•Median = 50
th
percentile

90. Percentile Example
•You scored 560 on the GMAT exam. This
score puts you in the 58
th
percentile.
•What percentage of test takers scored lower
than you did?
•What percentage of test takers scored higher
than you did?

91. Percentile Example
•What percentage of test takers scored lower
than you did?
58% of test takers scored lower than 560.
•What percentage of test takers scored higher
than you did?
(100 – 58)% = 42% of test takers scored
higher than 560.

92. Numerical Data
Properties & Measures
Mean
Median
Mode
Range
Variance
Standard Deviation
Interquartile Range
Numerical Data
Properties
Central
Tendency
Variation
Percentiles
Relative
Standing
Z–scoresZ–scores

93. Numerical Measures of
Relative Standing: Z–Scores
•Describes the relative location of a
measurement compared to the rest of the data
Sample z–score
x – x
s
z =
Population z–score
x – μ
σ
z =
Measures the number of standard deviations
away from the mean a data value is located

94. Z–Score Example
•The mean time to assemble a
product is 22.5 minutes with a
standard deviation of 2.5 minutes.
•Find the z–score for an item that
took 20 minutes to assemble.
•Find the z–score for an item that
took 27.5 minutes to assemble.

95. Z–Score Example
x = 20, μ = 22.5 σ = 2.5
x – μ 20 – 22.5
σ
z =
=
2.5
= –1.0
x = 27.5, μ = 22.5 σ = 2.5
x – μ 27.5 – 22.5
σ
z =
=
2.5
= 2.0

96. Quartiles & Box Plots

97. Quartiles
1.Measure of noncentral tendency
25%25%25%25% 25%25% 25%25%
QQ
11 QQ
22 QQ
33
2. Split ordered data into 4 quarters
Positioning Point ofQ
in
i

1
4
()
3. Position of i-th quartile

98. Quartile (Q
1) Example
•Raw Data:10.34.98.911.76.37.7
•Ordered:4.96.37.78.910.311.7
•Position:123456
QPosition
Q
1




 

1 1
4
161
4
1752
63
1
n()()
.
.

99. Quartile (Q
2) Example
•Raw Data:10.34.98.911.76.37.7
•Ordered:4.96.37.78.910.311.7
•Position:123456
QPosition
Q
2








2 1
4
261
4
35
7789
2
83
2
n()()
.
. .
.

100. Quartile (Q
3) Example
•Raw Data:10.34.98.911.76.37.7
•Ordered:4.96.37.78.910.311.7
•Position:123456
QPosition
Q
3




 

3 1
4
361
4
5255
103
3
n()()
.
.

101. Numerical Data
Properties & Measures
Mean
Median
Mode
Range
Interquartile RangeInterquartile Range
Variance
Standard Deviation
Skew
Numerical Data
Properties
Central
Tendency
Variation Shape

102. Interquartile Range
1.Measure of dispersion
2.Also called midspread
3.Difference between third & first quartiles
•Interquartile Range = Q
3 – Q
1
4.Spread in middle 50%
5.Not affected by extreme values

103. Thinking Challenge
•You’re a financial analyst for
Prudential-Bache Securities.
You have collected the
following closing stock prices
of new stock issues: 17, 16,
21, 18, 13, 16, 12, 11.
•What are the quartiles, Q
1
and Q
3, and the interquartile

range?

104. Q
1
Raw Data: 1716211813161211
Ordered: 1112131616171821
Position: 12345678
Quartile Solution*
QPosition
Q
1






1 1
4
181
4
25
125
1
n()()
.
.

105. Quartile Solution*
Q
3
Raw Data: 1716211813161211
Ordered: 1112131616171821
Position: 12345678
Q Position
Q
3




 

3 1
4
381
4
6757
18
3
n()()
.

106. Interquartile Range Solution*
Interquartile Range
Raw Data: 1716211813161211
Ordered: 1112131616171821
Position: 12345678
Interquartile Range   Q Q
3 1
18012555. . .

107. Box Plot
1.Graphical display of data using 5-number
summary
Median
44 66 88 1010 1212
Q
3
Q
1
X
largest
X
smallest

108. Shape & Box Plot
Right-SkewedLeft-Skewed Symmetric
QQ
11
MedianMedian QQ
33
QQ
11
MedianMedian QQ
33 QQ
11
MedianMedian QQ
33

109. Graphing Bivariate
Relationships

110. Graphing Bivariate
Relationships
•Describes a relationship between two
quantitative variables
•Plot the data in a Scattergram
Positive
relationship
Negative
relationship
No
relationship
x xx
yy y

111. Scattergram Example
•You’re a marketing analyst for Hasbro Toys.
You gather the following data:
Ad $ (x)Sales (Units) (y)
1 1
2 1
3 2
4 2
5 4
•Draw a scattergram of the data

112. Scattergram Example
0
1
2
3
4
0 1 2 3 4 5
Sales
Advertising

113. Time Series Plot

114. Time Series Plot
•Used to graphically display data produced
over time
•Shows trends and changes in the data over
time
•Time recorded on the horizontal axis
•Measurements recorded on the vertical axis
•Points connected by straight lines

115. Time Series Plot Example
•The following data shows
the average retail price of
regular gasoline in New
York City for 8 weeks in
2006.
•Draw a time series plot
for this data.
Date
Average
Price
Oct 16, 2006$2.219
Oct 23, 2006$2.173
Oct 30, 2006$2.177
Nov 6, 2006$2.158
Nov 13, 2006$2.185
Nov 20, 2006$2.208
Nov 27, 2006$2.236
Dec 4, 2006$2.298

116. Time Series Plot Example
2,05
2,1
2,15
2,2
2,25
2,3
2,35
10/16 10/23 10/30 11/6 11/13 11/20 11/27 12/4
Date
Price

117. Distorting the Truth
with Descriptive Techniques

118. Errors in Presenting Data
1.Using ‘chart junk’
2.No relative basis in
comparing data
batches
3.Compressing the
vertical axis
4.No zero point on the
vertical axis

119. ‘Chart Junk’
Bad PresentationBad Presentation Good PresentationGood Presentation
1960: $1.00
1970: $1.60
1980: $3.10
1990: $3.80
Minimum Wage Minimum Wage
0
2
4
1960197019801990
$

120. No Relative Basis
Good PresentationGood Presentation
A’s by Class A’s by Class
Bad PresentationBad Presentation
0
100
200
300
FRSOJRSR
Freq.
0%
10%
20%
30%
FRSOJRSR
%

121. Compressing
Vertical Axis
Good PresentationGood Presentation
Quarterly Sales Quarterly Sales
Bad PresentationBad Presentation
0
25
50
Q1Q2Q3Q4
$
0
100
200
Q1Q2Q3Q4
$

122. No Zero Point
on Vertical Axis
Good PresentationGood Presentation
Monthly Sales Monthly Sales
Bad PresentationBad Presentation
0
20
40
60
JMMJSN
$
36
39
42
45
JMMJSN
$

123. Conclusion
1.Described Qualitative Data Graphically
2.Described Numerical Data Graphically
3.Explained Numerical Data Properties
4.Described Summary Measures
5.Analyzed Numerical Data Using Summary
Measures