The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL STOR 155 Introductory Statistics Lecture 1 Overview Displaying Distributions with Graphs 5 11 10 Lecture 1 1 Tip Strategy for Success Stay active involved in class Ask questions during class especially if you do not understand something Answer questions to help other students if you can Keep pace with the lectures review daily do homework after each lecture to help understand the materials Make effective use of office hours Instructor open tutorial sessions UNC Learning Center Help you answer questions about homework and lectures Private time vs public time 5 11 10 Lecture 1 2 What is Statistics Statistics the science of collecting organizing analyzing and interpreting data information Population Inference about population using statistical tools Sample of data 5 11 10 Lecture 1 3 SAT Scores Some parents and teachers have been concerned about the trend of declining SAT scores Question effect of classroom atmosphere strict or liberal To answer the question 50 students 24 males and 26 females participated in a study on their performance as measured by SAT scores at the end of the school year The students were divided into two groups of 25 each 12 males and 13 females with Group 1 to study under a strict atmosphere while Group 2 under a very permissive atmosphere They were matched according to socio economic background 5 11 10 Lecture 1 4 SAT Scores After 9 months all students were given the same standardized tests verbal and math Student A B C D 5 11 10 Group Gender Strict F Strict M Liberal F Liberal M Lecture 1 SATMath 670 700 750 690 SATVer 700 680 730 750 5 SAT Scores This example involves data collection data analysis and statistical inference How Questions Does stricter classroom atmosphere increase the average score Why matched according to socio economic background Why 12 males and 13 females per group Is the group size 50 large enough to make a confident conclusion 5 11 10 Lecture 1 6 Fundamental Concepts Population the entire group of individuals that we want information about Students who are about to take SAT Sample a part of the population that we actually examine in order to gather information those students selected into the study Sample size number of observations individuals in a sample 50 Statistical inference to make an inference about a population based on the information contained in a sample Based on the data from the study to infer whether a stricter classroom atmosphere increases SAT scores in general 5 11 10 Lecture 1 7 Fundamental Concepts A parameter is a value that describes the population It s fixed but unknown in practice the average SAT score of all the students who are about to take SAT A statistic is a value that describes a sample It s known calculated from the sample the average SAT score of all the students who are selected into the study a sample analogue of the parameter 5 11 10 Lecture 1 8 Practice Exercise Suppose you are interested in finding the average SAT score of UNC unders SAT scores of all UNC unders in STOR155 sample SAT scores of all UNC unders population Suppose you are interested in finding the average SAT score of US unders SAT scores of all UNC unders SAT scores of all US unders 5 11 10 Lecture 1 9 Summary Statistics is the science of data Collecting Organizing and analyzing Decision making Information processing Fundamental concepts Population parameter sample statistic sample size You can do a LOT with statistics what 5 11 10 Lecture 1 10 Take home message Interested in population but it s too large to become known completely Statisticians work on sample which is a smaller and observable proxy There is uncertainty in this transition hence errors are inevitable That s why statistical methods are needed 5 11 10 Lecture 1 11 Chapter 1 Looking at Data Distributioins 1 1 Displaying Distributions with Graphs 1 2 Displaying Distributions with Numbers 1 3 Density Curves and Normal Distributions 5 11 10 Lecture 1 12 Data contain Individuals the subjects described by the data Variables any characteristic of an individual A variable can take different values for different individuals 5 11 10 Lecture 1 13 Categorical Quantitative Variables A categorical variable places an individual into one of several groups or categories A quantitative variable takes numerical values for which arithmetic operations such as adding and averaging make sense 5 11 10 Lecture 1 14 NBA Draft 2005 Name Team Nationality Weight Height A Bogut Milwaukee Australia 245 7 0 M Williams Atlanta US 230 6 9 D Williams Utah US 210 6 3 C Paul New Orleans US 175 6 0 R Felton Charlotte US 198 6 1 Categorical variables Team Nationality Quantitative variables Weight Height 5 11 10 Lecture 1 15 NBA Draft 2005 Variables Team Nationality Categorical Weight Height Quantitative How many teams in the draft How many players drafted by each team How many players higher than 6 9 How many players between 200 and 250 pounds Equivalently what is the distribution for each variable 5 11 10 Lecture 1 16 Distributions of Variables The distribution of a variable indicates what values a variable takes and how often it takes these values For a categorical variable distribution categories count percent for each category For a quantitative variable distribution pattern of variation of its values 5 11 10 Lecture 1 17 Highest Level of Education for People Aged 25 34 Education Count millions Percent Less than high school 4 6 11 8 High school graduate 11 6 30 6 Some college 7 4 19 5 Associate degree 3 3 8 8 Bachelor s degree 8 6 22 7 Advanced degree 2 5 6 6 5 11 10 Lecture 1 18 Exploratory Data Analysis EDA Use statistical tools and ideas to help us examine data Goal to describe the main features of the data NEVER skip this EDA Displaying distributions with graphs Displaying distributions with numbers 5 11 10 Lecture 1 19 Basic Strategies for EDA Strategy I 1 One variable at a time 2 Relationships among the variables Strategy II 1 Graphical visualizations 2 Numerical summaries 5 11 10 Lecture 1 20 Graphic Techniques for Categorical Variables Bar Graph uses bars to represent the frequencies or relative frequencies such that the height of each bar equals the frequency or relative frequency of each category Frequencies counts Relative frequencies percent height indicates count or percent Pie Chart is a circle divided into a number of slices that represent the various categories such that the size of each slice is proportional to the percentage
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