Sample and PopulationsThe population is the set of subjects in which we are interested.The sample is the subset of the population for whom we have(or plan to have) data.Examples:• General Social Survey (GSS): sample 4510, population alladult Americans (>200 million)• California exit poll: sample 2705, population all CA voters(≈7 million)A census is a complete enumeration.1Descriptive and Inferential StatisticsDescriptive statistics refers to methods for summarizing thedata. The summaries usually consist of graphs and numberssuch as averages and percentages.Interential statistics refers to methods for making predictionsor decisions about a population, based on data obtained from asample of that population.Example — confidence intervals. Of 834 people in a survey,54.0% say they favor handgun control. Using statistical meth-ods, we deduce there is 95% confidence that the true proportionis between 50.6% and 57.4%.2Parameters and StatisticsA parameter is a numerical summary of the population.A statistic is a numerical summary of a sample taken from thepopulation.3Randomness and Variability• Opinion poll — randomly choose the sample• Clinical trial — randomly assign participants to treatment orcontrolSamples vary because people do (or if it’s not people we’re sam-pling, whatever it is we are)4Computers and Statistics• Calculators• Minitab, SPSS• Excel5EXPLORING DATA WITHGRAPHS AND NUMERICALSUMMARIES6A variable is any characteristic that is recorded for subjects in astudy.A variable is called categorical if each observation belongs toone of a set of categories.A variable is called quantitative if observations on it take numer-ical values that represent different magnitudes of the variable.7A quantitative variable is called discrete if its possible valuesform a set of separate numbers, such as 0,1,2,3,....,A quantitative variable is continuous if its possible values forman interval.In practice, the method of data analysis depends on the type ofvariable.8Frequency TablesEach observation falls in one of several categories.A frequency table is a table that summarizes the number ofobservations in each category.The category with the highest frequency is called the mode.Students in last year’s class (who declared a political allegiance):Party Frequency Proportion PercentageDemocrat 35 0.515 51.5%Independent 12 0.176 17.6%Republican 21 0.309 30.9%Total 68 1.000 100%9The proportion of observations that fall in a certain category isthe frequency (count) of observations in that category dividedby the total number of observations. The percentage is theproportion multiplied by 100. Proportions and percentages arealso called relative frequencies.10Describing Data Using GraphicalSummaries1. Categorical Data2. Quantitative Data11Graphs for Categorical Variables• Pie charts• Bar graphs12Pie chart13Bar graph14Segmented bar graph15Segmented bar graph expressed as
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