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Course: STAT 051, Fall 2010School: GWU
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2 Descriptive Chapter Statistics Contents Introduction Qualitative Data Frequency Distribution Graphical Methods Quantitative Data Graphical Methods Numerical Summary Box Plot 2 Qualitative Data Measurements that cannot be measured on a natural numerical scale Observations can be classified into one of a group of categories Examples: a)Political affiliation (Democrat, Republican, etc) b)Rating of a...
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2
Descriptive Chapter Statistics
Contents
Introduction Qualitative Data Frequency Distribution Graphical Methods Quantitative Data Graphical Methods Numerical Summary Box Plot
2
Qualitative Data
Measurements that cannot be measured on a natural numerical scale Observations can be classified into one of a group of categories Examples:
a)Political
affiliation (Democrat, Republican, etc) b)Rating of a service (excellent, good, poor etc.) c)Race d)Gender
3
Summarizing Qualitative Data
Tabular Summary Frequency Distribution Relative Frequency Distribution Graphical Summary
Bar
Chart Pie Chart
4
Frequency Distribution
A FREQUENCY DISTRIBUTION is a tabular summary of data showing different classes and the frequency (or number) of items in each of several non-overlapping classes. It shows how the observations in the sample are distributed The objective is to provide insights about the data that cannot be quickly obtained by looking only at the original data.
5
Example 1.0
Students taking a distance learning course were asked to rate the quality of the course as being excellent, good, average, below average, or poor. The ratings provided by a sample of 20 students are shown below. Average Good Excellent Excellent Below Average Good Average Average Good Average Good Good Good Poor Average Good Below average Good Good Poor
6
Avg
Below Good Good Avg Good Good
Good Poor Avg Good
Below Good Good Poor
Example 1.0
Frequency Distribution: Shows 5 different classes(from 5 levels of the rating variable) and frequency for each class.
Good
Exclnt Avg Exclnt Avg
Rating Poor Below Average Average Good Excellent Total
Frequency 2 2 5 9 2 20
7
Relative Frequency Distribution
RELATIVE FREQUENCY of a class is the proportion of the total number of observations belonging to the class. Tabular Summary
Relative Frequency Distribution Frequency Distribution
Rating Poor Poor Avg Below Bverage Aelow Avg Average Good Gxcellent E ood Excellent Total Total
Relative Frequency F 2 requency 0.10 2/20 0.10 2/20 5 0.25 5/20 9 0.45 9/20 2 0/20 20 .10 1.00 20/20
8
Bar graphical Chart
A method for depicting qualitative data (from a frequency, relative frequency distribution.) n the horizontal axis the levels of the qualitative O variable are specified. ertical axis represents frequency or relative V frequency. ar of fixed width are drawn for each class, with B height being proportional to the frequency. he bars are separated T
9
Example 1.0 (Bar Chart)
Rating Rating Poor Below Average Average Good Rreq F el. Freq 2 0.10 2.10 0
Relative Frequency Bar Chart Frequency Bar Chart
5.25 0 9.45 0
Excellent 2.10 0 Total 20 1.0
10
Pie Chart
The PIE CHART is a graphical method used for presenting relative frequency distributions for qualitative data. A circle represents the entire dataset. It is partitioned so that each sector represents a class. Area of the sectors represent the relative frequency of class it is representing. 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.
11
Example 1.0 (contd)
Rating Poor Below Average Average Good Rel. Freq 0.10 0.10
9 0o
Poor Below Avg Average Good Excellent
0.25 0.45
Excellent 0.10 Total 1.0
12
Example 2.0
The following Dataset refers to a report published by Forbes magazine. In addition to income data Forbes collected and reported personal data on the CEOs, including level of education. The following data represent the highest degree obtained for the top 25 highest paid CEOs of 1999.
13
CEODEGREES
DATA:
Bachelors Bachelors Bachelors none Doctorate Masters Doctorate Masters JD Masters Masters Masters Masters Masters Bachelors Bachelors Bachelors Masters Masters Bachelors Masters LLB JD LLB Masters
14
Example 2.0
Variable: CEO degree We want see the distribution of the highest degree of CEOs of different companies. IN SPSS open the dataset: Then, Select: Graphs followed by BAR / PIE
15
Using SPSS : Dataset
16
Bar Chart: SPSS
12 10
Degrees of CEOs
COUNT
8 6
4 2 0
Bachelors Doctorate JD LLB Masters None
DEGREE
17
Pie Chart : SPSS
None Bachelors
Masters Doctorate JD LLB
18
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GWU - STAT - 051
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