Isom 2500 – Cheat Sheet
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ISOM 2500 1st Midterm Exam Revision NotesStatistics Terms Population：A group of all items of interest under studyCensus: Survey that includes every member in the populationParameter: A numerical descriptive measure of a populationSample: A part of populationStatistic: A numerical descriptive measure of a sampleVariable: is some characteristic of a population or a sampleData/Datum: Observed values of a variableObservations/Case: The set of measurements obtained for a particular elementElements: Entities on which data are collectedTypes of VariablesCategorical/Qualitative variable: Non-numerical variablesNumerical/Quantitative variable: Numerical DataDiscrete Variables: Variables that are integersCategorical/Qualitative variableNumerical/Quantitative variableNominal DataInterval DataOrdinal DataRatio DataContinuous Variables: Variables can be any real numberNominal Data: Applies to data that are divided into different groups (E.g. Gender)**Note that only calculations based on frequencies or % percentages of occurrence are validOrdinal Data: A type of nominal data where can be sorted or ranked. **Note that the data may be treated as nominal but not as intervalInterval Data: Applies to data that can be sorted and for which the difference can be counted and interpreted, has an arbitrarily-defined zero. **Note that an interval data can be treated as ordinal or nominal as wellRatio Data: Applies to data that can be sorted and for which the difference and ratio can be calculated and interpreted, has non-arbitrarily defined zero.ElementsVariablesPeriod of TimeCross-sectional dataDifferentN/ASameTime series dataSameSameDifferentPanel or longitudinal dataDifferentDifferentDifferentDescribing One Categorical Variable[pic 1][pic 2][pic 3][pic 4]
Tabular Display – Frequency distribution[pic 5]Graphical Display: Pie chart, bar chartRelative frequency of a category = [pic 6]Percent relative frequency of a category = [pic 7][pic 8]Describing Two Categorical VariablesTabular Display: Contingency Table Graphical Display: Cluster bar chartDescribing One numerical variableTabular Display: Frequency distribution // Summary tableGraphical display: Dotplot, Stem and Leaf diagram, histogram, polygon and Ogive The number of observations falling in each class is called the class frequencySteps for constructing a frequency distribution for numerical variable:Sort the dataDetermine the range where range equals to the largest observation minus the smallest observationDetermine the number of classes k using Sturges’ formula: , where n is the sample size, round up the k.[pic 10][pic 9]Divide the range by k to determine the class width[pic 11][pic 12]Determine the class limits[pic 13]DotplotA horizontal scale on which dots are placed to show the numerical values of the data points. If a value repeats, the dots will pile up at that location, one dot for one repetition.**Note that the dotplot is only useful for small sample size where n is less than 30Stem-and-Leaf DiagramA partly tabular//graphical way of summarizing data and it is suitable for moderate to large data sets (usually less than 100 observations)[pic 14]HistogramA bar chart for numerical values whose areas are proportional to relative frequencies of respective classes, for the sample size greater than or equal to 30. Note that the shapes of histograms can be bell-shaped, positively-skewed or negatively-skewed.[pic 15][pic 16][pic 17][pic 18][pic 19][pic 20][pic 21][pic 22][pic 23][pic 24][pic 25][pic 26][pic 27][pic 28]For sample size less than 30For less than 100 observationsFor sample size greater than 30DotplotStem-and-Leaf DiagramHistogramPolygon