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Mastering Frequency Distributions for Data Analysis

Understand frequency distributions, from categorical to grouped types. Learn the nuances of class limits vs. boundaries, class width, midpoint, relative & cumulative frequencies. Enhance your data presentation skills!

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Mastering Frequency Distributions for Data Analysis

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  1. FREQUENCY DISTRIBUTIONS

  2. What is a frequency distribution? • Presentation of raw or listed data into table form showing the variable and its frequencies. (Fancy word for a table!) • 3 types • Categorical • Ungrouped • Grouped For quantitative variables

  3. Example of a Categorical Frequency Distribution Rating of a Sociology Professor

  4. Example of an Ungrouped Frequency Distribution Scores on a 10 point Quiz

  5. Example of a Grouped Frequency Distribution Tread Depth of Tires

  6. Properties of the Grouped Frequency Distribution

  7. General Rules for a Well-Constructed Grouped F.D. • Generally use between 5 and 20 classes. • Classes must be mutually exclusive. (Can’t overlap with the same number) • Classes must be continuous. (Can’t skip any numbers) • Classes must be exhaustive. (Must use all of the data) • Classes must be the same width. (exception: open-ended distribution)

  8. Class Limits vs. Class Boundaries 0 - 3.5 3.5 – 7.5 7.5 – 11.5 11.5 – 15.5 15.5 – 19.5 *Boundaries show the continuous nature of the distribution. *Boundaries should be used when you have variables that included decimal values like height and weight

  9. Limits vs. Boundaries • Each of the following represents the limits of oneclass in a grouped frequency distribution. Find the boundaries for each class. • A) 20 – 29 • B) 300 – 399 • C) 5.5 – 6.5 • D) 67.2 – 68.2 19.5 – 29.5 299.5 – 399.5 5.45 – 6.55 67.15 – 68.25

  10. Finding Class Width *To find the width of a class, subtract any two consecutive lower class limits. *Remember class width should be uniform Throughout the table. Class width = 4

  11. Finding Class Midpoint 1.5 5.5 9.5 13.5 17.5 To find the midpoint of a class, find the average of the upper and lower limits of that class. Note: You can also find the first midpoint and then Add the class width.

  12. Relative Frequency Proportion of each frequency out of the total (n). Can be expressed as a decimal or a percent you don’t need to show all 3 values . decimal or % is fine Tread Depth of Tires 4/52=.077 or 7.7% 15/52=.288 or 28.8% 25/52=.481or 48.1% 5/52=.096 or 9.6% 3/52=.058 or 5.8% n = 52

  13. Cumulative Frequency The sum of the frequencies accumulated up to that class. Tread Depth of Tires 4 4 + 15 =19 19 + 25 = 44 44 + 5 = 49 49 + 3 = 52

  14. Relative Cumulative Frequency The sum of the relative frequencies up to that classor the proportion of each cumulative frequency (last row should always be 100%) Tread Depth of Tires 7.7% 7.7% 7.7 + 28.8 = 36.5% 28.8% 36.5 + 48.1 = 84.6% 48.1% 84.6 + 9.6 = 94.2% 9.6% 94.2 + 5.8 = 100% 5.8%

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