STAT Exam 1 ReviewTuesday, May 6, 20141:36 AM TOPIC 1 EXPLORING DATA-Variable – a variable is any characteristic of an individual; can take different values for differentindividualsoUnivarate – data has one variableoBivariate – data has two variablesoMultivariate – data has three or more variablesoTwo 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 valuespossible (number of siblings)Continuous – take on any real numerical value over an interval (age)-Graphical toolsoBar 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 valueoPie chart (categorical) – categorical variablesoFrequency table (categorical) - oHistogram (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 (numberof siblings, hair length of boys, income)Skewed to left – tail on the left (hair length of girls, number of teeth)oBoxplot (quantitative) – with histogram-Summary statisticsoMean – sum of observations divided by number of observations (average)oMedian – midpoint of observations ordered from smallest to largesto5-number summaryoStandard deviationoVariance -ConceptsoPopulation – the entire group of interestoSample – a part of the population selected to draw conclusions about the entire population-Individual (subject) – a person or any specific object in a populationoParameter – a fixed number that describes the population (usually known)oStatistic – a number produced from a sample (used to estimate a population parameter)TOPIC 2 RELATIONSHIPS BETWEEN TWO QUANTITATIVE VARIABLES-Two continuous variablesoResponse variable (dependent variable) oExplanatory variableoInterpreting a scatter plotoCorrelation-Two discrete variablesoContingency tableoStacked bar chartsoAssociationoCausationoLurking variableoSpurious correlationTOPIC 3 PROBABILITY-ProbabilityoConditional probability-Addition rules-Multiplication rules-Independent events-Disjoint events-Venn/tree diagramTOPIC 4 PROBABILITY DISTRIBUTIONS-Probability model-Discrete probability models-Continuous probability distributions-Density curves-Uniform distributionoHeight of density curveoCalculate probability of an event-Normal distributionoMeanoStandard deviationoVarianceoEmpirical ruleoStandard z-tableoQQ plot-Binomial distributionoBernoulli trialsoBinomial coefficientoBinomial 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