The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL STAT 155 Introductory Statistics Midterm Exam 1 Review 9 19 06 Midterm Exam 1 Review 1 Midterm Exam 1 Thur 9 21 in class Get a couple of Scantron sheets Students stores 2 pencil Calculator Closed book closed notes 9 19 06 Midterm Exam 1 Review 2 What is Statistics for Statistics the science of collecting organizing and interpreting data Data collection Data analysis organize summarize data to bring out main features and clarify their underlying structure Inference and decision theory extract the info provided by the data and may be used as a guide for further action 9 19 06 Midterm Exam 1 Review 3 Fundamental concepts Population the entire group of individuals that we want information about Sample a part of the population that we actually examine in order to gather information Sample size number of observations individuals in a sample Statistical inference to make an inference about a population based on the information contained in a sample 9 19 06 Midterm Exam 1 Review 4 Data contain Individuals the objects described by the data Variable any characteristic of an individual A variable can take different values for different individuals A categorical variable places an individual into one of several categories A quantitative variable takes numerical values for which arithmetic operations such as adding and averaging make sense 9 19 06 Midterm Exam 1 Review 5 Distributions of Variables The distribution of a variable indicates what values the 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 9 19 06 Midterm Exam 1 Review 6 Examining distribution Overall Pattern Shape Graphical techniques to display distributions Bar graph Pie chart Stemplot Histogram Modes peaks of a distribution unimodal or multimodal Symmetric or skewed to left right 9 19 06 Midterm Exam 1 Review 7 Center Mean easy to calculate highly affected by outliers Median can be time consuming to calculate more resistant to a few extreme observations sometimes outliers robust Mode Mean and Median relative locations for skewed symmetric dist which one to use 9 19 06 Midterm Exam 1 Review 8 Spread Standard deviation and variance definition and calculation sum of deviations always equals 0 square or not why divided by n 1 Quartiles definition and calculation IQR rule to identify outliers five number summary boxplots comparison with histograms and stemplots Range IQR S D 9 19 06 Midterm Exam 1 Review 9 Deviations Outliers some values that fall outside the overall pattern IQR can help to identify outliers Modified boxplots Strategies Detect them investigate their causes correct them or delete them or give them individual attention Use resistant methods such as median to reduce the influence of the outliers 9 19 06 Midterm Exam 1 Review 10 Linear transformation form xnew a bx its effects on shape center and spread 9 19 06 Midterm Exam 1 Review 11 Density curves probability density function pdf properties of pdf comparison with histograms mode median mean quartiles and s d of density curves 9 19 06 Midterm Exam 1 Review 12 normal distributions shape symmetric around mean single peaked unimodal bell shaped center and spread the 68 95 99 7 rule only for normal distributions 9 19 06 Midterm Exam 1 Review 13 Standardization and z Scores Effects of standardization Standardization is a linear transformation Standardized values under any distribution always have mean 0 and s d 1 Effects on shape center and spread Linear transformation normal to normal 9 19 06 Midterm Exam 1 Review 14 Standard normal distribution z x normal probability calculation on the margin or inside the table pictures help 9 19 06 Midterm Exam 1 Review 15