1. How to build frequency tables For Categorical and Numerical data

2. 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.

3. 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}

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

5. 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

6. 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

7. 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.

8. 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.

9. 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

10. 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.

11. Frequency Table FromTo <Absolute f Relative % 8010048% 100120714 % 120140918 % 1401601326 % 160180918 % 180200510 % 20022036 %

12. 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.