Discrete Data data that can take on a countable number of possible values

Discrete data data that can take on a countable

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Discrete Data: data that can take on a countable number of possible values ­ Example: An advertiser asks 200 customers how many days per week they read the daily newspaper. ­ Relative Frequency: the proportion of total observations that are in a given category. Relative frequency is computed by dividing the frequency in a category by the total number of observations. The relative frequencies can be converted to percentages by multiplying by 100. ­ Relative frequency = Frequency of the i th value of the discrete variable (f i ) / Total number of observations (n) ­ k = the number of different values for the discrete variable ­ Developing Frequency Distribution for Discrete Data: ­ Step 1: List all possible values of the variable. If the variable is ordinal level or higher, order the possible values from low to high. ­ Step 2: Count the number of occurrences at each value of the variable and place this value in a column labeled “frequency”. ­ Use Relative Frequency equation and divide each frequency count by the total number of observations and place in a column headed “relative frequency”. ­ Grouped Data: ­ Continuous Data: Data whose possible values are uncountable and that may assume any value in an interval. ­ Discrete data with many possible outcomes (age, income, stock price) ­ Summarized in a grouped data frequency distribution ­ Data are organized in classes (discrete categories). ­ Criteria for Building Classes: ­ Mutually exclusive: Classes that do not overlap so that a data value can be placed in only one class. ­ All­Inclusive: A set of classes that contains all the possible data values ­ Equal Width: The distance between the lowest possible value and the highest possible value in each class is equal for all classes. ­ Avoid empty classes. ­ Steps for Grouping Data into classes: (Developing Frequency Distribution for Continuous Data) ­ Determine the number of classes.
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­ Many vs. Few: ­ Many (narrow class intervals): ­ May yield a very jagged distribution with gaps from empty classes ­ Can give a poor indication of how frequency varies across classes ­ Few (Wide class intervals): ­ May compress variation too much and yield a blocky distribution ­ Can obscure important patterns of variation ­ Rule of Thumb: between 5 and 20 classes ­ Another rule: 2 k >_ n ­ k = number of classes and is defined to be the smallest integer ­ n = number of data values ­ Establish class width. ­ Minimum Class Width = Largest Value ­ Smallest Value / Number of Classes ­ Round up to a more convenient class width (Always round up) ­ Determine the class boundaries for each class. ­ Class boundaries: the upper and lower values of each class ­ Determine the class frequency for each class. ­ Cumulative Frequency Distribution: a summary of a set of data that displays the number of observations with values less than or equal to the upper limit of each of its classes.
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