Transcript Section_02_2

Statistics 300:
Introduction to
Probability and Statistics
Section 2-2
Chapters 2 and 3
• Describing data
• Exploring data
• Comparing data
Describe or Infer?
• Descriptive statistics
• Inferential statistics
Descriptive Statistics
• Describe characteristics of
(statistics) data samples as
they are without extending
their meaning beyond the
data sample
• Chapters 2 through 6
Inferential Statistics
• Based on a sample or multiple
samples, make inferences
(judgments) about the
population(s) from which the
sample(s) came.
• Chapters 7 through 12
Descriptive Statistics
• Distribution
• Center
• Variation
• Position
Distribution
• How are the data spread out?
• Where are data plentiful?
• Where are data rarely found?
Daily Carbon Monoxide
Site Number 2045 : Hawthorne
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Frequency
100
80
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40
20
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CO (ppm)
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6.
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Data for the year 2000
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Daily Carbon Monoxide
Site Number 2160 : Pasadena
120
Frequency
100
80
60
40
20
0
9.
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8.
CO (ppm)
10
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7.
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Data for the year 2000
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Distribution
• Frequency tables
• Pictures
Frequency Tables
• Identify categories for the
data
– Nominal categories or
– Interval categories
• Count the number of
observations in each category
Frequency Tables
Interval Categories
• Class Limits
• Class Midpoints
• Class Boundaries
Lower
Class
Limit
Upper
Class
Limit
10
30
50
20
40
60
Relative Cumulative
Freq. Frequency Frequency
3
3
2
0.38
0.38
0.25
3
6
8
50
41
8
18
32
24
50
17
25
Cumulative
Relative
Class
Class
Frequency Boundaries midpoints
0.38
0.75
1.00
25
45
15
35
55
Class Limits
• Convenient values
representing the range of
values in a class
• Lower class limit
• Upper class limit
Class Midpoints
• Values that are midway
between the lower and upper
class limits of each class
• To compute, average the two
class limits
Class Boundaries
• Values that truly separate one
class from the next
• To compute: average the
upper class boundary and the
following lower class
boundary
Frequency Tables
• Frequency
• Relative frequency
• Cumulative frequency
• Cumulative relative frequency
Frequency
• Count of the observations that
belong to each class
Relative Frequency
• Frequency divided by the
total number of observations
Cumulative Frequency
• Sum of the frequencies in the
first class through the current
class
Cumulative Relative
Frequency
• Sum of the relative
frequencies in the first class
through the current class
Distribution
• Frequency tables
• Pictures
Pictures
• Histograms and Bar Charts
• Pareto Charts
• Pie Charts