Grouped Frequency Distribution Tables

Grouped Frequency Tables

Sorting Items into Grouped Frequency Table

• Example 1: 20 Items

  • Data: 5, 9, 11, 17, 12, 6, 4, 8, 9, 27, 2, 12, 31, 35, 16, 13, 10, 2, 32, 29
  • Groups:
    • 1 to 10
    • 11 to 20
    • 21 to 30
    • 31 to 40
  • Tally: (This would be manually filled in based on the data)
  • Frequency: (This would be manually filled in based on the tally; it represents the count of items in each group)

• Example 2: 25 Items

  • Data: 10, 43, 25, 34, 31, 9, 25, 30, 28, 12, 26, 19, 11, 8, 35, 41, 28, 19, 8, 21, 20, 47, 32, 28, 21
  • Groups:
    • 0 < x < 10
    • 10 < x < 20
    • 20 < x < 30
    • 30 < x < 40
    • 40 < x < 50
  • Tally: (This would be manually filled in based on the data)
  • Frequency: (This would be manually filled in based on the tally; it represents the count of items in each group)

Sorting Decimal Items into Grouped Frequency Table

• Example 3: 15 Items

  • Data: 19.2, 23.4, 12.6, 23.1, 19.9, 17.3, 20.5, 14.1, 21.8, 13.0, 6.3, 7.9, 20.5, 23.6, 19.0
  • Groups:
    • 0 < x < 5
    • 5 < x < 10
    • 10 < x < 15
    • 15 < x < 20
    • 20 < x < 25
  • Tally: (This would be manually filled in based on the data)
  • Frequency: (This would be manually filled in based on the tally; it represents the count of items in each group)

Homework: Critical Thinking

• Analyzing a grouped frequency distribution table to identify the mathematical operations used to obtain the values in different columns (e.g., calculating midpoints, cumulative frequencies, relative frequencies).
• For grouped data, the midpoint of each class interval is often calculated as: Midpoint = \frac{Lower\ Limit + Upper\ Limit}{2}
• Cumulative frequency is calculated by adding the frequencies of all the previous classes, up to the current class. It indicates the number of data points that fall below the upper limit of a particular class
• Relative Frequency: \frac{Frequency\ of\ the\ class}{Total\ number\ of\ observations}