STA6126 Chapter 3 - Chapter 3 Descriptive Statistics 3.1...

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STA6126 Chapter 3, page 1 Chapter 3 Descriptive Statistics 3.1 Tabular and Graphical Description of Data Depends on Type of Data Data: Here is a part of the data set to be used in the examples of this lecture. subj ge ag hi co dh dr tv sp ne ah ve pa pi re ab aa ld 1 m 32 2.2 3.5 0 5.0 3 5 0 0 n r 6 2 n n y 2 f 23 2.1 3.5 1200 0.3 15 7 5 6 y d 2 1 y y u 3 f 27 3.3 3.0 1300 1.5 0 4 3 0 y d 2 2 y y u 4 f 35 3.5 3.2 1500 8 5 5 6 3 n i 4 1 y y n 5 m 23 3.1 3.5 1600 10 6 6 3 0 n i 1 0 y n n 6 m 39 3.5 3.5 350 3 4 5 7 0 y d 2 1 y y u 7 m 24 3.6 3.7 0 .2 5 12 4 2 n i 2 1 y y y 8 f 31 3.0 3.0 5000 1.5 5 3 3 1 n i 2 1 y y y 9 m 34 3.0 3.0 5000 2 7 5 3 0 n i 1 1 y y u 10 m 28 4.0 3.1 900 2 1 1 2 1 y i 3 0 n y y 11 m 23 2.3 2.6 253 1.5 10 15 1 1 n r 5 1 n y y 12 f 27 3.5 3.6 190 3 14 3 7 0 n d 2 1 y y u 13 m 36 3.3 3.5 245 1.5 6 15 12 5 n d 1 1 y y y 14 m 28 3.2 3.2 500 6 3 10 1 2 n i 4 1 y n y 15 f 28 3.0 3.5 3500 1 4 3 1 0 n d 1 0 y y y Source: http://www.stat.ufl.edu/~aa/social/data.html a) Summarizing categorical data: Here is an output from Minitab that summarizes the data for political affiliation of students. pa Count Democrat 21 Independent 24 Republican 15 N= 60 This summary is not very informative for a reader. Let’s put a title and label the columns to make it easy to understand: Table – 1 Distribution of UF Students in STA6126 By Political Affiliation, Fall 1996 (n = 60) Political Affiliation Number of Students Percent of Students Democrat 21 35 Republican 24 25 Independent 15 40 Total 60 100 Source: http://www.stat.ufl.edu/~aa/social/data.html We may also show the above results in a graphical summary called a pie chart or a bar graph
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STA6126 Chapter 3, page 2 Figure – 1 Distribution of UF Students in STA6126 By Political Affiliation, Fall 1996 (n = 60) Democrat Independent Republican Category Pie Chart of pa Source: http://www.stat.ufl.edu/~aa/social/data.html Republican Democrat Independent 40 30 20 10 0 Political Affiliation Percent of Students Distribution of UF Students in STA6126 by Political Affiliation Source: http://www.stat.ufl.edu/~aa/social/data.html
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STA6126 Chapter 3, page 3 b) Summarizing Quantitative Data Here is a summary of ag = age of students as obtained from Minitab Tally for Discrete Variables: ag ag Count Percent 22 3 5.00 23 10 16.67 24 7 11.67 25 2 3.33 26 8 13.33 27 5 8.33 28 5 8.33 29 1 1.67 30 1 1.67 31 4 6.67 32 3 5.00 33 1 1.67 34 1 1.67 35 1 1.67 36 1 1.67 39 1 1.67 41 2 3.33 44 1 1.67 50 2 3.33 71 1 1.67 N= 60 This is not a good summary, especially when there are too many possible values of the random variable of interest.
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STA6126 Chapter 3 - Chapter 3 Descriptive Statistics 3.1...

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