Chapter 1 Chapter 2 Chapter 3 Confidence significance levels significance Confidence 1 Statistics is getting information from data Population group of all items of interest parameter Sample set of data drawn from population statistic Use statistics to make inferences about parameters Single Variable Two Variables Interval Data Histogram Scatter plot Nominal Data Frequency relative frequency tables bar and pie chart Cross classification table bar chart Interval data quantitative numerical real numbers such as height weight income distances etc Nominal data categorical qualitative something arbitrary is assigned a number to a category 1 married 2 widowed etc Ordinal data appear to be nominal but their values have meaning poor 1 fair 2 good 3 etc Width of classes for histogram largest observation smallest observation of classes Sturge s Formula of class intervals 1 3 3log n Describing histograms modality skewness and symmetry bell shaped Ogive cumulative relative frequency use classes last class should 1 calculate rel freq calculate cum rel freq by adding current class s rel freq to the previous class Cross sectional observations measured at one point in time Time series observations measured over successive points in time Scatter plot describe strength and direction Chapter 4 Measures of central location mean median mode Population mean xi N Sample mean x bar xi n o Mean seriously affected by outliers best for describing measurement data o Median gets rid of outliers o Mode mostly used for nominal data For ordinal nominal data mean is not valid use median Geometric mean growth rate or rate of change overtime Measures of variablility o o o Range largest observation smallest observation Variance Standard deviation population 2 xi 2 N population sample s2 xi x bar 2 n 1 sample s population CV standard deviation mean Bell shaped histogram empirical rule 68 1 sd 95 2sd 99 7 3sd Chebysheff s rule applies to all histograms 1 1 k2 for k 1 k sd Coefficient of variation Location of percentile Lp n 1 P 100 Lp is the pth percentile IQR Q3 Q1 Sample covariance sxy xi xbar yi ybar n 1 when 2 variables move in the same direction covariance is large positive Coefficient of correlation r sxy sxsy Least squares method y hat b0 b1x 2 b1 sxy sx b0 yhat b1xbar sample cv s x bar Chapter 5 Methods of collecting data direct observation experiments surveys Sampling o o Simple random sample sample selected so that every possible sample of the same size is equally likely to be chosen drawing from a hat Stratified random sample obtained by separating the population into strata and then drawing srs s from them gender age occupation etc Cluster sample simple random sample of groups of clusters of elements vs a simple random sample of individual objects Types of errors o o Sampling error INCREASE SAMPLE SIZE differences between sample and population that exist only because of the observations that happened to be selected o Non sampling error increasing sample size will NOT reduce this error Errors in data acquisition clerical error incorrect measurements being taken because of equipment mistakes during transcription of notes inaccurate recordings etc Nonresponse errors introduced when responses are not obtained from some members in the sample Selection bias occurs when the sampling plan is such that some members cannot possibly be selected for inclusion in the sample Population N 2 CV xy Sample n xbar s2 s cv Sxy r Size Mean Variance Standard Deviation Coefficient of Variation Covariance Coefficient of Correlation Shortcut formulas SAMPLE COVARIANCE SAMPLE VARIANCE