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Saturday, November 29, 2014STAT*2060 Final Exam1. IntroductionStatistics- science of collection, classifying, summarizing, analyzing and interpretingdataDescriptive Statistics- numerical and graphical methods used to analyze, interpretand represent dataInferential Statistics- use information from a sample to make generalizations about apopulationQuantitative Data -numerical data that can be measured•use histograms, box plots and stem & leaf plots•Discrete Data -measurements can only take specific values•ex. number of rooms in a residence•Continuous Data -measurements can take any value within a specific range•ex. height, weight, time•Others include:Ordinal, Interval, Ratio dataQualitative Data -can not be measured on a numerical scale and data falls intocategories•ex. Favourite flavour of ice cream•use bar charts and pie charts to plot informationObservational Studies -we observe units and take measurements without assigningtreatmentsExperimental Studies -treatments are assigned to units and then the effects areobserved and measuresPopulation -large group of units that we are interested in studyingSample -a subset of the populationParameter -numerical characteristic of a population (usually not known)Statistic (estimator) -numerical characteristic of a sample (known)1
Saturday, November 29, 2014Statistical Inference -to calculate estimators of population parameters, and to quantifythe accuracy of these estimators with probabilitiesBiased Sampling•Selection Bias -sample is not representative of the population because a subsetof the population has no chance of being selected for the sample•Non Response Bias -there may be a reason that certain respondents refuse toparticipate•Measurement Error -the response measured and recorded for an individual unitis not correctRandom Sample -each unit in a population has an equal chance of being selected2. Descriptive StatisticsSample Variance and Sample Standard Deviation•measures of spread relative to the mean•SD is used more often when describing data because variance the units are squared•non negative (greater than or equal to zero)Histograms•graphical way to represent (quan) data•we make class intervals (equal/varying width) which contains data of interest•count the frequency at which we observe data falling into one of these classintervals and construct a frequency table•Relative Frequency = frequency (height)/midpoint of intervalSkewness•measure of how much a distribution leans towards a particular side or whether it issymmetric•Symmetric- observations cantered around mean and tail of evenly on both sides•Right (Positively) Skewed- tail to the right side of the mean and more observationsconcentrated on smaller values2
Saturday, November 29, 2014•mean > median•Left (negatively) Skewed- tail to the left side of the mean with more observationsconcentrated on larger values•mean < medianQuartiles•First Quartile (Q1) - 25% of observations lie below this value (25th percentile)•