STAT Exam 1 Review Tuesday May 6 2014 1 36 AM TOPIC 1 EXPLORING DATA Variable a variable is any characteristic of an individual can take different values for different individuals o Univarate data has one variable o Bivariate data has two variables o Multivariate data has three or more variables o Two types Categorical place an individual into one of several groups Nominal purely qualitative and unordered UIN ID SSN zip code area code gender treatment group car color Ordinal can be ranked movie ratings star ratings Numerical quantitative take on numerical values for which arithmetic makes sense Discrete take on only certain fixed values with no intermediate values possible number of siblings Continuous take on any real numerical value over an interval age Graphical tools o Bar graph categorical describing a single categorical variable Frequency number of times the value occurs in the data gives the distribution Relative frequency proportion of the data with the value o Pie chart categorical categorical variables o Frequency table categorical o Histogram quantitative two quantitative variables Shape symmetric skew to right left number of modes or peaks Center around mean or median Spread from minimum to maximum the range x axis Symmetric normal bell shaped curve girls weight age Skewed to right tail on the right mean is larger than median number of siblings hair length of boys income Skewed to left tail on the left hair length of girls number of teeth o Boxplot quantitative with histogram Summary statistics o Mean sum of observations divided by number of observations average o Median midpoint of observations ordered from smallest to largest o 5 number summary o Standard deviation o Variance Concepts o Population the entire group of interest o Sample a part of the population selected to draw conclusions about the entire population Individual subject a person or any specific object in a population o Parameter a fixed number that describes the population usually known o Statistic a number produced from a sample used to estimate a population parameter TOPIC 2 RELATIONSHIPS BETWEEN TWO QUANTITATIVE VARIABLES Two continuous variables o Response variable dependent variable o Explanatory variable o Interpreting a scatter plot o Correlation Two discrete variables o Contingency table o Stacked bar charts o Association o Causation o Lurking variable o Spurious correlation TOPIC 3 PROBABILITY Probability o Conditional probability Addition rules Multiplication rules Independent events Disjoint events Venn tree diagram TOPIC 4 PROBABILITY DISTRIBUTIONS Probability model Discrete probability models Continuous probability distributions Density curves Uniform distribution o Height of density curve o Calculate probability of an event Normal distribution o Mean o Standard deviation o Variance o Empirical rule o Standard z table o QQ plot Binomial distribution o Bernoulli trials o Binomial coefficient o Binomial probability Normal approximation for binomial distributions As a rule of thumb use normal appx When n is so large that mean np 10 failure mean n 1 p
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