l01-10 - What Is Statistics? The department of study that...

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What Is Statistics? The department of study that has for its object the collection and ar- rangement of numerical facts or data, whether relating to human affairs or to natural phenomena. (Oxford English Dictionary) The science of collecting, organizing, and interpreting numerical facts, which we call data. (Moore and McCabe) The science of collecting, describing, and interpreting data. (Johnson and Kuby) Why Statistics? Some Goals of This Class Becoming an informed consumer of information Understanding data analysis done by others Learning to perform your own analysis - 2 -
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Some definitions Individual (Unit): each object described by a set of data Variable: any characteristic of an individual ± Categorical variable: places an individual into one of several groups or categories. ± Quantitative variable: takes numerical values on which we can do arithmetic. Distribution of a variable: tells what values it takes and how often it takes these values. Example: The following data set consists of five variables about 20 individuals. ID Age Education Sex Total income Job class 1 43 4 1 18526 5 2 35 3 2 5400 7 3 43 2 1 3900 7 4 33 3 1 28003 5 5 38 3 2 43900 7 6 53 4 1 53000 5 7 64 6 1 51100 6 8 27 4 2 44000 5 9 34 4 1 31200 5 10 27 3 2 26030 5 11 47 6 1 6000 6 12 48 3 1 8145 5 13 39 2 1 37032 5 14 30 3 2 30000 5 15 35 3 2 17874 5 16 47 4 2 400 5 17 51 4 2 22216 5 18 56 5 1 26000 6 19 57 6 1 100267 7 20 34 1 1 15000 5 Age: age in years Education: 1=no high school, 2=some high school, 3=high school diplom, 4=some college, 5=bachelor’s degree, 6=postgraduate degree Sex: 1=male, 2=female Total income: income from all sources Job class: 5=private sector, 6=government, 7=self employed Variables Age and Total income are quantitative, variables Eduction , Sex , and Job class are categorical. - 3 -
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Categorical variable analysis Questions to ask about a categorical variable: How many categories are there? In each category, how many observations are there? Bar graphs and pie charts Categorical data can be displayed by bar graphs or pie charts . In a bar graph , the horizontal axis lists the categories, in any order. The height of the bars can be either counts or percentages. For better comparison of the frequencies, the variables can be ordered from most frequent to lest frequent. In a pie chart , the area of each slide is proportional to the percentage of individuals who fall into that category. Example: Education of people aged 25 to 34 0 10 20 30 Percent of people aged 25 to 34 no HS some HS HS diploma Bachelor’s some college postgrad Education level HS diploma Bachelor’s some college postgrad some HS no HS Education level 3.6% 7.5% 30.4% 29.1% 22.7% 6.7% no HS some HS HS diploma Bachelor’s some college postgrad - 4 -
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Quantitative variables: stemplots Example: Sammy Sosa home runs R commands > hr<-read.table("hr.txt", header=TRUE) > attach(hr) > stem(HR,scale=2) Stem-and-leaf plot for HR 0 | 48 1 | 05 2 | 5 3 | 366 4 | 009 5 | 0 6 | 346 Year Home runs 1989 4 1990 15 1991 10 1992 8 1993 33 1994 25 1995 36 1996 40 1997 36 1998 66 1999 63 2000 50 2001 64 2002 49 2003 40 How to make a stemplot 1. Separate each observation into a stem and a leaf.
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l01-10 - What Is Statistics? The department of study that...

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