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Discrete Data: data that can take on a countable number of possible valuesExample: An advertiser asks 200 customers how many days per weekthey read the daily newspaper.Relative Frequency: the proportion of total observations that are in a givencategory. Relative frequency is computed by dividing the frequency in a categoryby the total number of observations. The relative frequencies can be converted topercentages by multiplying by 100.Relative frequency = Frequency of theith value of the discrete variable (fi)/ Total number of observations (n)k = the number of different values for the discrete variableDeveloping Frequency Distribution for Discrete Data:Step 1: List all possible values of the variable. If the variable is ordinallevel or higher, order the possible values from low to high.Step 2: Count the number of occurrences at each value of the variableand place this value in a column labeled “frequency”.Use Relative Frequency equation and divide each frequency count by thetotal number of observations and place in a column headed “relativefrequency”.Grouped Data:Continuous Data: Data whose possible values are uncountable and thatmay assume any value in an interval.Discrete data with many possible outcomes (age, income, stock price)Summarized in a grouped data frequency distributionData are organized in classes (discrete categories).Criteria for Building Classes:Mutually exclusive: Classes that do not overlap so that a data value canbe placed in only one class.AllInclusive: A set of classes that contains all the possible data valuesEqual Width: The distance between the lowest possible value and thehighest possible value in each class is equal for all classes.Avoid empty classes.Steps for Grouping Data into classes: (Developing Frequency Distribution forContinuous Data)Determine the number of classes.
Many vs. Few:Many (narrow class intervals):May yield a very jagged distribution with gaps fromempty classesCan give a poor indication of how frequency variesacross classesFew (Wide class intervals):May compress variation too much and yield ablocky distributionCan obscure important patterns of variationRule of Thumb: between 5 and 20 classesAnother rule: 2k>_ nk = number of classes and is defined to be the smallestintegern = number of data valuesEstablish class width.Minimum Class Width = Largest Value Smallest Value / Numberof ClassesRound up to a more convenient class width (Always roundup)Determine the class boundaries for each class.Class boundaries: the upper and lower values of each classDetermine the class frequency for each class.Cumulative Frequency Distribution: a summary of a set of data that displays thenumber of observations with values less than or equal to the upper limit of eachof its classes.