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How to build frequency tables For Categorical and Numerical data

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Frequency Tables: Categorical Rows are called classes Each categorical (discrete) value occupies its own class Then frequency is counted for each class in absolute (#) and in relative (%) terms.

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Example Variable: Gender Nature: Categorical, Nominal. Values: Male, Female Raw Data: {M, M, F, M, M, F, F, F, F, F, M, M, F, F, F, F, M, M, F, F}

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Gender Frequency Distribution GenderAbsolute Frequency Relative Frequency Male88/20 = 40% Female1212/20 = 60% Total2020/20 = 100%

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Frequency Tables: Numerical Rows are called classes The number of classes, c, is a function of the number of observations, n: C = 1 + 3.3*LOG(n) –Sturges law If n = 50, then c 6.6

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Frequency Tables: Numerical Each class consists of a range of values know as the class width, w. The class width must be the same for all classes. W = Range ÷ c, where Range = MAX-MIN If MIN = 82 and MAX = 213 for n=50 observations, then: W = (213 – 82) / 6.6 20

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Frequency Tables: Lower Class Limits To build classes, we then start measuring class widths FROM a nice (round) number smaller than MIN. The LOWER CLASS LIMITS are c numbers that are 1 class width, w, greater than the previous one.

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Frequency Tables: Upper Class Limits UPPER CLASS LIMITS mark ending values for each class. They are smaller in value than the LOWER CLASS LIMITS of the previous classes.

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Frequency Tables: Value Classes Example Example: 2.12 on page 57, UTILITY Data: n=50, MIN=82, MAX=213 Range = 213 – 82 = 131 C = 1 + 3.3*LOG(50) 7 W = 131 / 7 20 Frequency Table Class Limits: FromTo < 80100 120 140 160 180 200 220

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Frequency Table: absolute and % counts To complete a frequency table we then tally how many observations in a data set fall in each of the previously formed class ranges. These tallies can be accounted for in units or in % of the total number of observations, n.

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Frequency Table FromTo

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Frequency Tables: using PhStat To count frequencies, all you do is let PhStat do the tallying for you, using the command sequence: PhStat Descriptive Statistics Frequency Distribution … Then, you input the proper cell ranges in the dialog box for the procedure: Variable cell range: range of cells for data. Bins cell range: class limits for classifying data.

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Copyright © Cengage Learning. All rights reserved. 2 Organizing Data.

Copyright © Cengage Learning. All rights reserved. 2 Organizing Data.

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