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Statistics

STAB22H3

Moras

Winter

Description

record of experiencesobservations is called datastatistics is preoccupied with the collection and analysis of data for the purpose of learning and understandinga variable is a characteristic of the individualsrows are called cases or individualsvariables classified as either quantitative or categoricalquantitative variables take number valuescategorical variables assign individuals to categories distribution of a variable is the different values the variable can take together wit how often it takes those valuesdescriptions of patterns on a graph can include shapesymmetrypeaksskewness centrelocation on x axis variabilityspread on x axis outliersdepartures from overall patterngraphical descriptions of categorical variables include barchartpiechartbarchart y axiscounts of variable that falls into categories x axisvalues the variable can takepiechart depicts percentages of beers in categories limited in that it needs to use every category in datasetgraphical descriptions of quantitative variables include stemplotshistogramsboxplots bin denotes the length of an interval in a histogramfrequency histogram denotes the count on y axisrelative frequency histograms denotes the proportion of individuals on y axisin density histograms the area of the bar denotes the proportion of individuals with observed valuequantitative variables are usually described using center and spread of distributioncenter is calculated with sample meansample medianspread is calculated with sample standard deviationsample IQRsample mean describes the average calculated with xxxnsample mean is sensitive to skew and outliers used to describe the center of a 1nsymmetric distributionsample median is not sensitive to skew and is calculated by n12 used to describe distributions with skewednesssample standard deviation describes average deviation from the average value denoted by s sensitive to skew and outliers describes symmetric distributionsquartiles have four landmarks in an ordered datasetQ1 hasof the data being less than it Q2M Q3 hasof the data larger than itIQRQ3Q1 describe spread not sensitive to skew15IQR is a measure of skew suspected outliers above 15IQRQ3suspected outliers below Q115IQRhistogram is a statistical model based on data for the distribution of a quantitative variabledensity curves are the mathematical model analogous to the statistical density histograma normal density curve hasmu andsigma standard density curve has 0 1notation for normal distribution XNthe 6895997 rule describes standard deviation of 123 respectively states that all normal density curves are similar in the way that area Is distributed under themuse standardization formula to find area under the curve zx using a table of standard normal probabilities you can find PZ such that Z is greater or less than the calculated numberthe joint distribution of two variables is the possible combinations of values that they take together with how often they take those combinations of valuesit is the association between two variables that is captured in a joint distribution that is missing from the respective separate distributionsthe statistical procedure of prediction is called regressionin a scatter plot you are looking to describe the typedirectionstrength of associationthe type of association refers to proposing a function of best fit linearpolynomialexponentialdirection of association is positive or negativestrength of the association refers to how tightly packed dots are around the proposed curve the sample correlation can be used to measure the strength of linear associations denoted by r r1n1 E xxsyys where xy are sample ixiymeans and sxsy are sample standard deviations and xiyi are the aggregated coordinate values capital sigmar 1 describes a very strong linear association and r0 describes no linear associationa variable is called the explanatory variable if it explains or causes the variability in the other variablethe other variable would be the response variablea regression equation is any formula that you get from the data for the purposes of predicting the response or the mean response from knowledge of the value of the explanatory variablethe functional form of the regression line is yb bx 0 1where y is the notation for the predicted value of the response variable or the predicted value of the mean responseb1 has the interpretation of being the predicted mean change in the response variable for a 1 unit increase in the explanatory variableGauss recognized calculus techniques could be used achieve a best fitting regression line least

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